 Mathematics
 556 (Registered)

This is a collegelevel calculus course designed to meet the Advanced Placement curricular requirements for Calculus BC (equivalent to one year of college calculus). The major topics of this course are limits, derivatives, integrals, the Fundamental Theorem of Calculus, and series. We will investigate and analyze course topics using equations,
graphs, tables, and words, with a particular emphasis on a conceptual understanding of calculus. Applications, in particular to solid geometry and physics, will be studied where appropriate.
Students must have access to a graphing calculator at all times. Students are required to have a TINSpire CX CAS.
Course Content

Chapter 1 Prerequisites for Calculus 0/6

Lecture1.1Lines

Lecture1.2Functions and Graphs

Lecture1.3Exponential Functions

Lecture1.4Parametric Equations

Lecture1.5Functions and Logarithms

Lecture1.6Trigonometric Functions


Chapter 2 Limits and Continuity 0/4

Lecture2.1Rates of Change and Limits

Lecture2.2Limits Involving Infinity

Lecture2.3Continuity

Lecture2.4Rates of Change and Tangent Lines


Chapter 3 Derivatives 0/9

Lecture3.1Derivative of a Function

Lecture3.2Differentiability

Lecture3.3Rules for Differentiation

Lecture3.4Velocity and Other Rates of Change

Lecture3.5Derivatives of Trigonometric Functions

Lecture3.6Chain Rule

Lecture3.7Implicit Differentiation

Lecture3.8Derivatives of Inverse Trigonometric Functions

Lecture3.9Derivatives of Exponential and Logarithmic Functions


Chapter 4 Applications of Derivatives 0/6

Lecture4.1Extreme Values of Functions

Lecture4.2Mean Value Theorem

Lecture4.3Connecting ƒ’ and ƒ” with the Graph of ƒ

Lecture4.4Modeling and Optimization

Lecture4.5Linearization and Newton’s Method

Lecture4.6Related Rates


Chapter 5 The Definite Integral 0/5

Lecture5.1Estimating with Finite Sums

Lecture5.2Definite Integrals

Lecture5.3Definite Integrals and Antiderivatives

Lecture5.4Fundamental Theorem of Calculus

Lecture5.5Trapezoidal Rule


Chapter 6 Differential Equations and Mathematical Modeling 0/5

Lecture6.1Slope Fields and Euler’s Method

Lecture6.2Antidifferentiation by Substitution

Lecture6.3Antidifferentiation by Parts

Lecture6.4Exponential Growth and Decay

Lecture6.5Logistic Growth


Chapter 7 Applications of Definite Integrals 0/5

Lecture7.1Integral As Net Change

Lecture7.2Areas in the Plane

Lecture7.3Volumes

Lecture7.4Lengths of Curves

Lecture7.5Applications from Science and Statistics


Chapter 8 Sequences, L’Hôpital’s Rule, and Improper Integrals 0/4

Lecture8.1Sequences

Lecture8.2L’Hôpital’s Rule

Lecture8.3Relative Rates of Growth

Lecture8.4Improper Integrals


Chapter 9 Infinite Series 0/5

Lecture9.1Power Series

Lecture9.2Taylor Series

Lecture9.3Taylor’s Theorem

Lecture9.4Radius of Convergence

Lecture9.5Testing Convergence at Endpoints


Chapter 10 Parametric, Vector, and Polar Functions 0/3

Lecture10.1Parametric Functions

Lecture10.2Vectors in the Plane

Lecture10.3Polar Functions

Instructor
David is the professor of mathematics education at David School and a former Associate Professor of Physics at JNTU. He served as a teacher of mathematics and Physics in various international schools in Asia and Europe. His research focuses on social and cultural factors as well as educational policies and practices that facilitate mathematics engagement, learning, and performance, especially for underserved students. David School collaborates with teachers, schools, districts, and organizations to promote mathematics excellence and equity for young people.
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