Courses Taught

Click course title for more information

At Amherst College

As Instructor

• Introduction to Analysis: SP19, F19, SP20, SP21, F22, SP23, SP24, F24
• Measure Theory and Integration: SP24
• Real Analysis in Higher Dimensions: SP20
• Linear Algebra: F22, SP23, F23, F24
• Transition to Theoretical Mathematics: F18, SP19
• Intermediate Calculus: F23
• Introduction to the Calculus: F18
• Calculus with Algebra: F20

At the University of Pittsburgh

As Instructor

• Introduction to Theoretical Mathematics: F17
  (Introduction to proofs for math majors/minors)
  ×

  Introduction to Theoretical Mathematics

  Course Description:
  This course is an introduction to writing mathematical proofs, including discussion of mathematical notation, methods of proof, and strategies for formulating and communicating mathematical arguments.
  

  Class Information:
  3 one hour lectures per week
  2 one hour recitations per week
  3 Exams
  Weekly written homework assignments
  Weekly in-class presentations
  Avg. Class Size: 25 students
  

  Textbook:
  Personal Notes.
  Basic Analysis by Jiří Lebl. (Loosely used)
  
  

  Topics Covered:
  

  • Chapter 1: Logic, proofs and quantifiers. Basic set theory. Functions. Equivalence relations. Elementary properties of the natural numbers; mathematical induction. Axiomatic introduction to the ordered fields of rational and real numbers. Elementary inequalities. The Completeness Axiom; Archimedean Property of the real numbers; density of the rational and irrational numbers in the real numbers. The Completeness Axiom; Archimedean Property of the real numbers; density of the rational and irrational numbers in the real numbers. Countability of the rationals; decimal expansions of real numbers; uncountability of the real numbers.
  • Chapter 2: Sequences and an introduction to series; the geometric series; limits; Limit Laws. The Monotone Convergence Theorem. The Bolzano-Weierstrass Theorem. Cauchy sequences; Cauchy completeness of the real numbers. Series; convergence tests; alternating series; conditional convergence and rearrangements.
  • Chapter 3: Cluster points; limits of functions; continuous functions and examples of sets of points of discontinuity.

  Course Resource Page
• Ordinary Differential Equations I: SP16
  (Proof-based course for math majors/minors)
  ×

  Ordinary Differential Equations

  Course Description:
  This course is devoted to studying the well-posedness of certain nth order linear and nonlinear ordinary differential equations.
  

  Class Information:
  2 one and half hour lectures per week
  3 Exams
  Weekly written homework assignments
  Avg. Class Size: 22 students
  

  Textbook:
  Elementary Differential Equations and Boundary Value Problems Tenth Edition by William E. Boyce and Richard C. DiPrima supplemented with Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard.
  
  

  Topics Covered:
  

  • Chapter 2: Linear Equations; Method of Integrating Factors, Separable Equations, Modeling with First Order Equations, Exact Equations and Integrating Factors, and Numerical Approximations: Euler's Method, Huen's Formula, Runge
  • Chapter 3: Homogeneous Equations with Constant Coefficients, Solutions of Linear Homogeneous Equations; the Wronskian, Complex Roots of the Characteristic Equation, Repeated Roots; Reduction of Order, Non-homogeneous Equations; Method of Undetermined Coefficients, Variation of Parameters, and Reduction of Order
  • Chapter 5: Cauchy-Euler Equations, Series Solutions of nth Order Linear and First Order Nonlinear Equations
  • Chapter 7: Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors, The Theory of Systems of First Order Linear Equations, Homogeneous Linear Systems with Constant Coefficients, and Nonhomogeneous Linear Systems, and The Matrix Exponential
  • Chapter 8: Numerical Approximations: The Euler/Tangent Line Method, Improved Euler's Method/Huen's Formula, and Runge-Kutta Method
  • Chapter 9: The Phase Plane: Linear Systems, Autonomous Systems and Stability, Linearization of Nonlinear Systems, Predator-Prey Equations, and Lyapunov’s Second Method

• Calculus I: F15, F16, F17
  ×

  Calculus I

  Course Description:
  Calculus I is the first course in the basic calculus sequence and is intended for all mathematics, engineering, science, and statistics students. Topics covered include the derivatives and integrals of functions of a single variable. A lab component in which students apply numeric, algebraic, and graphing technologies to calculus problems is an central part of the course.
  

  Class Information:
  3 one-hour Lectures per week
  2 Exams and 1 Final Exam
  Weekly online homework assignments via LON CAPA (a free course management system developed at Michigan Sate University)
  Weekly in-class quizzes
  Avg. Class Size: 75 students
  

  Textbook:
  Essential Calculus: Early Transcendentals, second edition, by James Stewart
  
  

  Topics Covered:
  

  • Chapter 1: Functions and their representations, the limit of a function, calculating limits, continuity, infinite limits, and limits at infinity.
  • Chapter 2: Derivatives and rates of change, the derivative as a function, basic differentiation formulas and rules, the product and quotient rules, the chain rule, implicit differentiations, related rates, and linear approximations.
  • Chapter 3: Exponential functions, inverse functions and logarithms, derivatives of logarithmic and exponential functions, inverse trigonometric functions, hyperbolic functions, indeterminate forms and l'Hospital's rule.
  • Chapter 4: Maximum and minimum values, The Mean Value Theorem, derivatives and the shapes of graphs, curve sketching, optimization problems, Newton's Method, Antiderivatives
  • Chapter 5: Areas and Distances, the definite integral, The Fundamental Theorem of Calculus and evaluating definite integrals, substitution rule (change of variables)
  • Chapter 6: Integration by parts, trigonometric integrals, and trigonometric substitution.

  Course Resource Page
• Calculus II: F15, SP17
  ×

  Calculus II

  Course Description:
  Calculus II is the second installment in the basic calculus sequence and is intended for all mathematics, engineering, science, and statistics students. Broadly speaking, topics covered include integration techniques, applications of the integration, sequences and series, parametric equations, polar coordinates, and an introduction to vector arithmetic and the topic of differential equations.
  

  Class Information:
  3 one-hour Lectures per week
  2 Exams and 1 Final Exam
  Weekly online homework assignments via LON CAPA (a free course management system developed at Michigan Sate University)
  Weekly in-class quizzes
  Avg. Class Size: 75 students
  

  Textbook:
  Essential Calculus: Early Transcendentals, second edition, by James Stewart
  
  

  Topics Covered:
  

  • Chapter 6: Substitution Rule (Change of Variables), Integration by Parts, Trigonometric Integrals, Trigonometric Substitution, The Method of Partial Fractions, and Improper Integrals.
  • Chapter 7: Calculating Areas Between Curves, Volumes via Discs/Washers and Cylindrical Shells, and Arc Length
  • Chapter 8: Sequences, Series, The Integral Test and Estimates of Sums, The Comparison Tests, Alternating Series, Absolute Convergence and the Ratio and Root Tests, Strategy for Testing Series, Power Series, Representations of Functions as Power Series, Taylor and Maclaurin Series, and Applications of Taylor Polynomials
  • Chapter 9: Parametric Curves, Calculus with Parametric Curves, Polar Coordinates, and Areas and Lengths in Polar Coordinates
  • Chapter 10: 3D Coordinate Systems, Vectors, The Dot Product, The Cross Product and, Equations of Lines and Planes
  • Additional Topics: Linear Equations; Method of Integrating Factors, Separable Equations, Modeling with First Order Equations, Second Order Homogeneous Linear Equations with Constant Coefficients, Second Order Non-Homogeneous Linear Equations with Constant Coefficients; Method of Undetermined Coefficients,

At the University of Missouri - Columbia

As Instructor

• Calculus III: SP14
  ×

  Calculus III

  Course Description:
  This course is devoted to the study of vectors, solid analytic geometry, and calculus of several variables.
  

  Class Information:
  3 one-hour Lectures per week
  3 Exams and 1 Final Exam
  Weekly online homework assignments via WebAssign
  Weekly in-class quizzes
  Avg. Class Size: 28 students
  

  Textbook:
  Multivariable Calculus, 7th edition, by James Stewart
  
  

  Topics Covered:
  

  • Chapter 12: 3D Coordinate Systems, Vectors, The Dot Product, The Cross Product and, Equations of Lines and Planes
  • Chapter 13: Vector Functions and Space Curves, Derivatives and Integrals of Vector Functions, Arc Length and Curvature, and Motion in Space - Velocity and Acceleration
  • Chapter 14: Functions of Several Variables, Partial Derivatives, Tangent Planes and Linear Approximations, The Chain Rule, Directional Derivatives and the Gradient Vector, Maximum and Minimum Values, and The Method of Lagrange Multipliers
  • Chapter 15: Double Integrals over Rectangles, Iterated Integrals and Fubini's Theorem, Double Integrals over General Regions, Double Integrals in Polar Coordinates, Applications of Double Integrals, Triple Integrals, Triple Integrals in Cylindrical and Spherical Coordinates, and Change of Variables in Multiple Integrals
  • Chapter 16: Vector Fields, Line Integrals, The Fundamental Theorem for Line Integrals, Green's Theorem Curl and Divergence, Parametric Surfaces and their Areas, Surface Integrals, Stokes' Theorem, and The Divergence Theorem

• Ordinary Differential Equations I: SS12, SP15
  ×

  Ordinary Differential Equations

  Course Description:
  This course is devoted to studying the well-posedness of certain first and second-order ordinary differential equations.
  

  Class Information:
  3 one-hour Lectures per week
  3 Exams and 1 Final Exam
  Bi-monthly written homework assignments
  Weekly in-class quizzes
  Avg. Class Size: 28 students
  

  Textbook:
  Elementary Differential Equations and Boundary Value Problems (Custom Edition for the Math. Dept. of the University of Missouri-Columbia) Tenth Edition by William E. Boyce and Richard C. DiPrima
  
  

  Topics Covered:
  

  • Chapter 2: Linear Equations; Method of Integrating Factors, Separable Equations, Modeling with First Order Equations, Exact Equations and Integrating Factors, and Numerical Approximations: Euler's Method, Huen's Formula, Runge
  • Chapter 3: Homogeneous Equations with Constant Coefficients, Solutions of Linear Homogeneous Equations; the Wronskian, Complex Roots of the Characteristic Equation, Repeated Roots; Reduction of Order, Non-homogeneous Equations; Method of Undetermined Coefficients, Variation of Parameters, Mechanical and Electrical Vibrations, and Forced Vibrations
  • Chapter 6: Definition of the Laplace Transform, Solution of Initial Value Problems, Step Functions, Differential Equations with Discontinuous Forcing Functions, Impulse Functions, and The Convolution Integral
  • Chapter 7: Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors, The Theory of Systems of First Order Linear Equations, Homogeneous Linear Systems with Constant Coefficients, and Nonhomogeneous Linear Systems, and The Matrix Exponential
  • Chapter 8: Numerical Approximations: The Euler/Tangent Line Method, Improved Euler's Method/Huen's Formula, and Runge-Kutta Method
  • Chapter 9: The Phase Plane: Linear Systems, Autonomous Systems and Stability, and Linearization of Nonlinear Systems

• College Algebra: F08, SP09, F09, SP10, F10, SP11, F13
  ×

  College Algebra

  Course Description:
  This course consists of a review of exponents, order of operations, factoring, and simplifying polynomial, rational, and radical expressions. Moreover, we will investigate the properties of linear, quadratic, polynomial, rational, inverse, exponential, and logarithmic functions as well as their applications.
  

  Class Information:
  General Education Requirement
  3-5 one-hour Lectures per week
  3 Exams and 1 Final Exam
  Weekly online homework assignments via WebWork
  Weekly in-class quizzes
  Bi-monthly online quizzes via WebWork
  Avg. Class Size: 30 students
  

  Textbook:
  College Algebra, by Carl Stitz and Jeff Zeager Full-Text PDF
  
  

  Topics Covered:
  

  • Review Chapter: Sets and Interval Notation, Real Number Arithmetic, Linear Equations and Inequalities, Absolute Value Equations and Inequalities, Polynomial Arithmetic, Factoring, Quadratic Equations, Rational Expressions and Equations, and Radicals and Equations
  • Chapter 1: The Cartesian Coordinate Plane, Introduction to Functions, Function Notation, Function Arithmetic, Graphs of Functions, and Transformations of Graphs of Functions
  • Chapter 2: Quadratic Functions and Inequalities with Quadratic Functions
  • Chapter 3: Polynomial Functions
  • Chapter 4: Introduction to Rational Functions, Graphs of Rational Functions, and Rational Inequalities
  • Chapter 5: Composition of Functions and Inverse Functions
  • Chapter 6: Introduction to Exponential and Logarithmic Functions, Properties of Logarithms, Exponential Equations and Logarithmic Equations

  Course Resource Page
• Calculus for Social and Natural Sciences: F10
  ×

  Calculus for Social and Natural Sciences

  Course Description:
  This course covers the real number system, functions, analytic geometry as well as an introduction to derivatives, integrals, and maximum-minimum problems.
  

  Class Information:
  For Business, Accounting, Nursing, etc. Majors
  3 one-hour Lectures per week
  3 Exams and 1 Final Exam
  Weekly online homework assignments via WebWork
  Weekly in-class quizzes
  Avg. Class Size: 30 students
  

  Textbook:
  Calculus and Its Applications, 12th edition, by L.J. Goldstein, D.C. Lay, D.I. Schneider, and N. Asmar
  
  

  Topics Covered:
  

  • Chapter 1: The Slope of a Straight Line, The Slope of a Curve at a Point, The Derivative, Some Rules for Differentiation, More About Derivatives, and The Derivative as a Rate of Change
  • Chapter 2: Describing Graphs of Functions, The First and Second Derivative Rules, Curve Sketching, and Optimization Problems
  • Chapter 3: The Product and Quotient Rules, The Chain Rule and the General Power Rule, Implicit Differentiation, and Related Rates
  • Chapter 4: Exponential Functions, The Exponential Function e^x, Differentiation of Exponential Functions, The Natural Logarithm Function, The Derivative of the Natural Logarithm Function, and Properties of the Natural Logarithm Function
  • Chapter 5: Exponential Growth and Decay, and Compound Interest
  • Chapter 6: Antidifferentiation, Areas and Riemann Sum, Definite Integrals and the Fundamental Theorem, Areas in the xy-Plane, and Applications of the Definite Integral

• Mathematics Prep Course for Summer Transitions Program: SS13
  ×

  Mathematics Prep Course for Summer Transitions Program

  Program Description:
  

  The Summer Transition Program (STP) is an academic learning community held during the 8-week Summer Session that bridges the gap between High School and College academic life. STP is aimed at offering first year, first time college students an opportunity to enroll in general education courses, participate in a residential living experience, and utilize campus resources to achieve success at The University of Missouri.

  Each day during this 8-week program, students focus on completing the ALEKS Prep and Learning Module in order to develop good study skills, build a solid foundation for future college level mathematics, and obtain college credit for some mathematics courses. ALEKS is a powerful artificial-intelligence based assessment tool that zeros in on the strengths and weaknesses of a student's mathematical knowledge, reports its findings to the student, and if necessary provides the student with a learning environment for bringing this knowledge up to an appropriate level for course placement. The University of Missouri requires an ALEKS mathematics placement assessment to determine readiness for various courses. The ALEKS Placement Assessment covers material from Basic Math concepts through Precalculus and will take approximately 90 minutes to complete. The main goal of the Mathematics Prep Course for the Summer Transitions Program is to work side by side with students to improve their mathematical skills and, in turn, their course placement.

  
  

  Software:
  ALEKS Prep and Learning Module
  
  

  Topics Covered:
  

  • Chapter 1: Addition with carry, Subtraction with borrowing, Multiplication/division with carry, Introduction to exponents, Order of operations, Equivalent fractions, Simplifying a fraction, Writing an improper fraction as a mixed number and vice versa, Ordering fractions, Addition/subtraction of fractions, Fraction multiplication/division, Mixed arithmetic operations with fractions, Rounding decimals, Decimal addition/subtraction, Decimal multiplication, and Converting a fraction to a terminating decimal
  • Chapter 2: Converting between percentages and decimals, Writing a ratio as a percentage, Percentage of a whole number, Solving a proportion of the form x/a = b/c, Word problems on proportions, Perimeter of a square or a rectangle, Finding a side length given the perimeter and side lengths with variables, Area of a geometric shapes: square or a rectangle, piecewise rectangular figure, triangle, and parallelogram, Finding the side length of a rectangle given its perimeter or area, Circumference and area of a circle, Area involving inscribed figures, Volume of a rectangular prism and cylinder, Surface area of a cube/rectangular prism and of a cylinder, Angles and Triangles, Solving equations involving vertical angles, and Similar polygons
  • Chapter 3: Absolute value of a number, Integer addition/subtraction, Exponents; integers, signed fractions, and order of operations, Writing a simple variable expression for a real-world situation, Evaluating a linear expression in two variables, Evaluating a quadratic expression in one variable, Distributive property, Combining like terms, Solving linear equations, Graphing a linear inequality on the number line, Graphing a compound linear inequality on the number line, Solving a linear inequality, Solving a compound linear inequality, and Solving an equation involving absolute value
  • Chapter 4: Plotting a point in the coordinate plane, Finding a solution to a linear equation in two variables, Graphing a line given its equation in slope-intercept/standard form, Graphing a vertical or horizontal line, Finding slope of a line, Slopes of parallel and perpendicular lines, Finding x- and y-intercepts of a line given the equation, Solving a system of linear equations using substitution and elimination, Graphing a linear inequality in the plane, and Graphing a system of linear inequalities
  • Chapter 5: Set builder and interval notation, Union and intersection of finite sets, Evaluating functions, Evaluating a piecewise-defined function, Sum, difference, and product of two functions, Domain and range of a function, Vertical line test, Finding local maxima and minima of a function given the graph, Transformations of the graph of a function, Composition of two functions, and Inverse functions
  • Chapter 6: Writing a number without a negative exponent, Product/Quotient/Power rule of exponents, Scientific notation, Addition/subtraction/Multiplication of Polynomials, and Factoring polynomials
  • Chapter 7: Solving quadratic equations/inequalities, Graphing a quadratic function, Finding zeros/x- and y-intercepts of a polynomial function, Determining the end behavior of the graph of a polynomial function, and Graphing a circle given its equation
  • Chapter 8: Simplifying rational expressions, Adding/subtracting/multiplying/dividing rational expressions, Complex fractions, Solving rational equations, Word problems on direct/inverse variation, Sketching the graph of a rational function
  • Chapter 9: Simplifying expressions with radicals, Solving equations with radicals, Pythagorean Theorem, Distance between two points in the plane, and Rational exponents
  • Chapter 10: Properties of logarithms, Solving logarithmic and exponential equations, The graph, domain, and range of logarithmic and exponential functions, and Solving a word problem using an exponential equation
  • Chapter 11: Converting between degree and radian measure, Sketching an angle in standard position, Reference angles, Coterminal angles, Arc length and central angle measure, Sine, cosine, and tangent ratios, Right triangle trigonometry with Sine, cosine, and tangent ratios and the laws of sines and cosines, The unit circle, Amplitude, period, and phase shift of sine and cosine functions, Sketching the graph of a sine or cosine function, Inverse trigonometric functions, Simplifying trigonometric expressions, Sum and difference identities, Double-angle identities, and Trigonometric equations

As a Teaching Assistant

• Analytic Geometry and Calculus I: F09, SP12
  ×

  Analytic Geometry and Calculus I

  Course Description:
  This course is devoted to the study of elementary geometry, functions, limits, continuity, derivatives, antiderivatives, and definite integrals.
  

  Class Information:
  3 one-hour Lectures and 2 one-hour discussions per week
  3 Exams and 1 Final Exam
  Weekly online homework assignments via WebAssign
  Weekly in-class quizzes
  Avg. Class Size: 300 students in lectures and 32 in discussions
  

  Textbook:
  Single Variable Calculus, 7th edition, by James Stewart
  
  

  Topics Covered:
  

  • Chapter 1: Ways to Represent a Function, Mathematical Models: A Catalog of Essential Functions, New Functions from Old Functions, The Tangent and Velocity Problems, The Limit of a Function, Calculating Limits Using the Limit Laws, The Precise Definition of a Limit, and Continuity
  • Chapter 2: Derivatives and Rates of Change, The Derivative as a Function, Differentiation Formulas, Derivatives of Trigonometric Functions, The Chain Rule, Implicit Differentiation, Rates of Change in the Natural and Social Sciences, Related Rates, and Linear Approximations and Differentials
  • Chapter 3: Maximum and Minimum Values, The Mean Value Theorem, Derivatives and the Shape of the Graph, Limits at Infinity: Horizontal Asymptotes, Curve Sketching, Optimization Problems, Newton's Method, and Antiderivatives
  • Chapter 4: Areas and Distances, The Definite Integral, The Fundamental Theorem of Calculus, Indefinite Integrals and the Net Change Theorem, and Change of Variables
  • Chapter 5: Areas Between Curves, Volumes by Washers and Cylindrical Shells

• Calculus II: F12, SP13, SP14, F14
  ×

  Calculus II

  Course Description:
  This course is devoted to the study of elementary transcendental functions, techniques and applications of integration, sequences, series, power series with applications, and parametric equations and polar coordinates.
  

  Class Information:
  3 one-hour Lectures and 2 one-hour discussions per week
  3 Exams and 1 Final Exam
  Weekly online homework assignments via WebAssign
  Weekly in-class quizzes
  Avg. Class Size: 32 students
  

  Textbook:
  Single Variable Calculus, 7th edition, by James Stewart
  
  

  Topics Covered:
  

  • Chapter 6: Inverse Functions, Exponential Functions and Their Derivatives, Logarithmic Functions, Derivatives of Logarithmic Functions, Inverse Trigonometric Functions, and Indeterminate Forms and L'Hospital's Rule
  • Chapter 7: Integration by Parts, Trigonometric Integrals, Trigonometric Substitution, Integration of Rational Functions by Partial Fractions, Strategy for Integration, and Improper Integrals
  • Chapter 8: Arc Length and Area of a Surface of Revolution
  • Chapter 10: Curves Defined by Parametric Equations, Calculus with Parametric Curves, and Polar Coordinates
  • Chapter 11: Sequences, Series, The Integral Test and Estimates of Sums, The Comparison Tests, Alternating Series, Absolute Convergence and the Ratio and Root Tests, Strategy for Testing Series, Power Series, Representations of Functions as Power Series, Taylor and Maclaurin Series, and Applications of Taylor Polynomials

• Calculus II Honors: SP13
  ×

  Calculus II Honors

  Course Description:
  This course is the writing intensive counterpart to Math 1700 (Calculus II) which emphasizes critical thinking in the study of elementary transcendental functions, techniques and applications of integration, sequences, series, power series with applications, and parametric equations and polar coordinates.
  

  Class Information:
  3 one-hour Lectures and 2 one-hour discussions per week
  1 Mid-term Exam and 1 Final Exam
  Weekly written homework assignments
  Weekly in-class quizzes
  Avg. Class Size: 27 students
  

  Textbook:
  Single Variable Calculus, 7th edition, by James Stewart
  
  

  Topics Covered:
  

  • Chapter 6: Inverse Functions, Exponential Functions and Their Derivatives, Logarithmic Functions, Derivatives of Logarithmic Functions, Inverse Trigonometric Functions, and Indeterminate Forms and L'Hospital's Rule
  • Chapter 7: Integration by Parts, Trigonometric Integrals, Trigonometric Substitution, Integration of Rational Functions by Partial Fractions, Strategy for Integration, and Improper Integrals
  • Chapter 8: Arc Length and Area of a Surface of Revolution
  • Chapter 10: Curves Defined by Parametric Equations, Calculus with Parametric Curves, and Polar Coordinates
  • Chapter 11: Sequences, Series, The Integral Test and Estimates of Sums, The Comparison Tests, Alternating Series, Absolute Convergence and the Ratio and Root Tests, Strategy for Testing Series, Power Series, Representations of Functions as Power Series, Taylor and Maclaurin Series, and Applications of Taylor Polynomials

• Advanced Calculus for One Real Variable: F12
  ×

  Advanced Calculus for One Real Variable

  Course Description:
  Rigorous introduction to foundations of real analysis; real numbers, point set topology in Euclidean space, functions, continuity, differentiation, and integration.
  

  Class Information:
  For advanced undergraduate and beginning graduate level students
  3 one-hour Lectures and 2 one-hour discussions per week
  3 Exams and 1 Final Exam
  Weekly written homework assignments
  Weekly in-class quizzes
  Avg. Class Size: 23 students
  

  Textbook:
  Introduction to Real Analysis, 4th Edition, by Robert G. Bartle and Donald R. Sherbert
  
  

  Topics Covered:
  

  • Chapter 1: Sets and Functions, Mathematical Induction, and Finite and Infinite Sets
  • Chapter 2: The Algebraic and Order Properties of the Real Line, Absolute Value and the Real Line, The Completeness Property of the Real Line, Applications of the Supremum Property, and Intervals
  • Chapter 3: Sequences and Their Limits, Limit Theorems, Monotone Sequences, Subsequences and the Bolzano-Weierstrass Theorem, The Cauchy Criterion, Properly Divergent Sequences, and an Introduction to Infinite Series
  • Chapter 4: Limits of Functions, Limit Theorems, and Some Extensions of the Limit Concept
  • Chapter 5: Continuous Functions, Combinations of Continuous Functions, Continuous Functions on Intervals, Uniform Continuity, Continuity and Gauges, and Monotone and Inverse Functions
  • Chapter 6: The Derivative, The Mean Value Theorem, L’Hospital’s Rules, and Taylor’s Theorem
  • Chapter 7: Riemann Integral, Riemann Integrable Functions, The Fundamental Theorem, The Darboux Integral, and Approximate Integration
  • Chapter 8: Pointwise and Uniform Convergence, Interchange of Limits, The Exponential and Logarithmic Functions, and The Trigonometric Functions
  • Chapter 9: Absolute Convergence, Tests for Absolute Convergence, Tests for Nonabsolute Convergence, and Series of Functions.
  • Chapter 11: Open and Closed Sets in R, Compact Sets, Continuous Functions, and Metric Spaces.

I recently started to teach using a Windows Surface Pro. Here is a video lecture of my Calculus I course at the University of Pittsburgh where I am using it.