Calculus, Third Edition
Revised July 17, 2004
Calculus, Third Edition
Hughes-Hallett, Gleason, McCallum et al
John Wiley & Sons, Inc., 2002
Table of Contents
(some subsection titles edited slightly; check with individual instructors for sections included in their specific classes since syllabi can vary)
CALCULUS I (MATH 2014) (Differential Calculus) TOPICS:
Syllabus from Shirley Pomeranz
Chapter 1. A Library of Functions
1. Functions and Change
2. Exponential Functions
3. New Functions from Old
4. Logarithmic Functions
5. Trigonometric Functions
6. Powers, Polynomials, and Rational Functions
7. Introduction to Continuity
Chapter 2. Key Concept: The Derivative
2.1 How Do We Measure Speed?
2.2 Limits
2.3 The Derivative at a Point
2.4 The Derivative Function
5. Interpretations of the Derivative
6. The Second Derivative
7. Continuity and Differentiability
Chapter 3. Short-Cuts to Differentiation
3.1 Powers and Polynomials
3.2 The Exponential Function
3.3 The Product and Quotient Rules
3.4 The Chain Rule
3.5 The Trigonometric Functions
3.6 Applications of the Chain Rule (More Differentiation Rules and Related Rates Problems)
3.7 Implicit Differentiation
3.8 Parametric Equations
3.9 Linear Approximation and the Derivative
3.10 Using Local Linearity to Find Limits (L’Hopital’s Rule)
Chapter 4. Using the Derivative
4.1 Using First and Second Derivatives (Sketching Graphs of Functions)
4.2 Families of Curves
4.3 Optimization
4.4 Application to Economics (Marginality) (This section is skipped)
4.5 Optimization and Modeling
4.6 Hyperbolic Functions (This section is skipped)
4.7 Theorems about Continuous and Differentiable Functions
Chapter 5. Key Concept: The Definite Integral
5.1 How Do We Measure Distance Traveled (Riemann Sums)
5.2 The Definite Integral
5.3 Interpretations of the Definite Integral
5.4 Theorems About the Definite Integral (Integration Rules)
Chapter 6. Constructing Antiderivatives
6.1 Antiderivatives Graphically and Numerically
6.2 Constructing Antiderivatives Analytically (Integration Rules)
END OF CALCULUS I TOPICS
CALCULUS II (MATH 2024) (Integral Calculus, etc.)TOPICS:
Note: Mathematica is Introduced in Calculus II Labs
Syllabus from Dale Doty
Chapter 6. Constructing Antiderivatives
6.1 Antiderivatives Graphically and Numerically
6.2 Constructing Antiderivatives Analytically (Integration Rules)
6.3 Differential Equations (Introduction to the Most Basic Differential Equations)
6.4 Second Fundamental Theorem of Calculus
6.5 The Equations of Motion
Chapter 7. Integration
7.1 Integration by Substitution
7.2 Integration by Parts
7.3 Table of Integrals
4. Algebraic Substitutions sand Trigonometric Substitutions
5. Approximating Definite integrals
6. Approximation Errors and Simpson’s Rule
7. Improper Integrals
8. Comparison of Improper Integrals
Chapter 8. Using the Definite Integral
8.1 Areas and Volumes
8.2 Applications to Geometry
8.3 Density and Center of Mass
8.4 Applications to Physics
8.5 Applications to Economics (This section is skipped)
8.6 Distribution Functions
8.7 Probability, Mean, and Median
Chapter 9. Series
9.1 Geometric Series
9.2 Convergence of Sequences and Series
9.3 Tests for Convergence
9.4 Power Series
Chapter 10. Approximating Functions
10.1 Taylor Polynomials
10.2 Taylor Series
10.3 Finding and Using Taylor Series
10.4 The Error in Taylor Polynomial Approximations
10.5 Fourier Series
Chapter 11. Differential Equations
11.1 What is a Differential Equation?
11.2 Slope Fields
11.3 Euler’s Method
11.4 Separation of Variables
11.5 Growth and Decay (This section is skipped)
11.6 Applications and Modeling (This section is skipped)
11.7 Models of Population Growth (This section is skipped)
11.8 Systems of Differential Equations (This section is skipped)
11.9 Analyzing the Phase Plane (This section is skipped)
11.10 Second-Order Differential Equations: Oscillations (This section is skipped)
11.11 Linear Second-Order Differential Equations (This section is skipped)
Additional Topics:
13.1 Displacement Vectors
13.2 Vectors in General
17.1 Parameterized Curves
17.2 Motion, Velocity, and Acceleration
Polar Coordinates (one class)
Complex Numbers (one class)
END OF CALCULUS II TOPICS
CALCULUS III (MATH 2073) (Multivariate Calculus) TOPICS:
Syllabus from Bill Hamill
Chapter 12. Functions of Several Variables
12.1 Functions of Two Variables
12.2 Graphs of Functions of Two Variables
12.3 Contour Diagrams
12.4 Linear Functions
12.5 Functions of Three Variables
12.6 Limits and Continuity
Chapter 13. A Fundamental Tool: Vectors
(These two sections are skipped now; Sections 13.1 Displacement Vectors and
13.2 Vectors in General are covered in Calculus II)
13.3 The Dot Product
13.4 The Cross Product
Chapter 14. Differentiating functions of Several Variables
14.1 The Partial Derivative
14.2 Computing Partial Derivatives Algebraically
14.3 Local Linearity and the Differential
14.4 Gradients and Directional Derivatives in the Plane
14.5 Gradients and Directional Derivatives in Space
14.6 The Chain Rule
14.7 Second-Order Partial Derivatives
14.8 Differentiability
Chapter 15. Optimization: Local and Global Extrema
15.1 Local Extrema
15.2 Optimization
15.3 Constrained Optimization: Lagrange Multipliers
Chapter 16. Integrating Functions of Several Variables
16.1 The Definite Integral of a Function of Two Variables
2. Iterated Integrals
3. Triple Integrals
4. Double Integrals in Polar Coordinates
5. Integrals in Cylindrical and Spherical Coordinates
6. Application of Integration to Probability
7. Change of Variables in a Multiple Integral
Chapter 17. Parameterization and Vector Fields
(These two sections are skipped now; Sections 17.1 Parameterized Curves and
17.2 Motion, Velocity, and Acceleration are covered in Calculus II)
17.3 Vector Fields
17.4 The Flow of a Vector Field
17.5 Parameterized Surfaces (This section is skipped)
Chapter 18. Line integrals
18.1 The Idea of a Line Integral
18.2 Computing Line Integrals Over Parameterized Curves
18.3 Gradient Fields and Path-Independent Fields
18.4 Path-Dependent Vector Fields and Green’s Theorem
Chapter 19. Flux Integrals
19.1 The Idea of a Flux Integral
19.2 Flux Integrals for Graphs, Cylinders, and Spheres
19.3 Flux Integrals Over Parameterized Surfaces (This section is skipped)
Chapter 20. Calculus of Vector Fields
20.1 The Divergence of a Vector Field
20.2 The Divergence Theorem
20.3 The Curl of a Vector Field
20.4 Stoke’s Theorem
20.5 The Three Fundamental Theorems
END OF CALCULUS III TOPICS
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