Math 1206 - Calculus

James E. Shockley
Department of Mathematics
Virginia Tech

Bring earphones to study these modules in the Math Emporium.

Text: Stewart, Calculus, Early Transcendentals, 5th Edition

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Some background topics are listed in the final table.

Chapter 4. Applications of Differentiation
Section Topic
4.4 L'Hopital's Rule -- Part 1
4.4 L'Hopital's Rule -- Part 2
4.10 Differential Equations
4.10 Gravitational Attraction

Chapter 5. Integrals
Section Topic
5.1 Sigma Notation
5.1 Formulas for Sums
5.1- 5.2 Riemann Sums and Area
5.2 The Definite Integral
5.2 Definite Integrals and Area
5.3 The Fundamental Theorem of Calculus I
5.3 The Fundamental Theorem of Calculus 2
5.3 Properties of The Definite Integral
5.4 The Indefinite Integral
5.5 Integration by Substitution
5.5 The Substitution Principle -- Examples
5.5 Substitution With Definite Integrals
5.6 The Natural Logarithm Function
5.6 Integrals Involving Natural Logarithms
5.6 The Exponential Function
5.6 Integrals Involving Exponential Functions
5.6 Exponents and Logarithms to Other Bases

Chapter 6. Applications of Integration
Section Topic
6.1 Area
6.1 Area Examples
6.2 The Disk Method
6.3 The Shell Method
6.3 Shell and Disk Problems
6.4 Work
6.4 Work -- Spring Problems
6.4 Work -- Pumping Problems

Chapter 7. Techniques of Integration
Section Topic
7.1 Integration by Parts -- Part 1
7.1 Integration by Parts -- Part 2
7.2 Trigonometric Integrals I
7.2 Trigonometric Integrals II
7.3 Trigonometric Substitution I
7.3 Trigonometric Substitution II
7.4 Partial Fractions I
7.4 Partial Fractions II
7.4 Partial Fractions III
7.7 The Trapezoidal Rule
7.7 Simpson's Rule
7.8 Improper Integrals -- Integrals Over Infinite Domains
7.8 Improper Integrals -- Integrals of Discontinuous Functions

Chapter 8. Further Applications of Integration
Section Topic
8.1 Arc Length
8.3 Moments Along a Line -- Finite Systems
8.3 Moments in the Plane -- Finite Systems
8.3 Moments of Thin Plates--Theory
8.3 Moments of Plane Regions--Examples

Additional Topics
Sections Topic
1.6, 5.6 One-to-One Functions
1.6, 5.6 Graphs of Inverse Functions
1.6 The Inverse Sine Function
3.6, 5.4 The Inverse Sine Function -- Derivatives and Integrals
1.6 The Inverse Tangent Function
3.6, 5.4 The Inverse Tangent Function -- Derivatives and Integrals
4.10 Family of Curves
6.5 The Mean Value Theorem for Integrals
8.3 Moments Along a Line --Thin Rods