Calculus II Curriculum Mapping
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The following is based on Thomas’ Calculus: Early Transcendentals, by Weir, Hass, and Thomas, 12th edition.
Module 1 Integration
1.1 Antiderivatives (Section 4.8)
1.2 Area and Estimating with Finite Sums (Section 5.1)
1.3 Sigma Notation and Limits of Finite Sums (Section 5.2)
1.4 The Definite Integral (Section 5.3)
1.5 The Fundamental Theorem of Calculus (Section 5.4)
1.6 The Substitution Method (Section 5.5)
1.7 Substitution and Area Between Curves (Section 5.6)
Module 2 Applications of Definite Integrals
2.1 Volumes Using Cross-Sections (Section 6.1)
2.2 Volumes Using Cylindrical Shells (Section 6.2)
2.3 Arc Length (Section 6.3)
2.4 Areas of Surfaces of Revolution (Section 6.4)
2.5 Work and Fluid Forces (Section 6.5)
2.6 Moments and Centers of Mass (Section 6.6)
Module 3 Techniques of Integration
3.1 The Logarithm as an Integral (Section 7.1)
3.2 Integration by Parts (Section 8.1)
3.3 Trigonometric Integrals (Section 8.2)
3.4 Trigonometric Substitutions (Section 8.3)
3.5 Integration of Rational Functions by Partial Fractions (Section 8.4)
3.6 Numerical Integration (Section 8.6)
3.7 Improper Integrals (Section 8.7)
Module 4 Series and Sequences
4.1 Sequences and Infinite Series (Sections 10.1, 10.2)
4.2 The Integral Test (Section 10.3)
4.3 Comparison Tests (Section 10.4)
4.4 The Ratio and Root Tests (Section 10.5)
4.5 Alternating Series, Absolute and Conditional Convergence (Section 10.6)
4.6 Power Series (Section 10.7)
4.7 Taylor and Maclaurin Series (Section 10.8)
4.8 Convergence of Taylor Series (Section 10.9)
4.9 Applications of Taylor Series (Section 10.10)
Module 5 Parametric Equations, Polar Coordinates and Vectors
5.1 Parametrizations of Plane Curves (Section 11.1)
5.2 Calculus with Parametric Curves (Section 11.2)
5.3 Polar Coordinates (Sections 11.3, 11.4)
5.4 Areas and Lengths in Polar Coordinates (Section 11.5)
5.5 Three-Dimensional Coordinate Systems and Vectors (Sections 12.1, 12.2)
5.6 The Dot Product (Section 12.3)
5.7 The Cross Product (Section 12.4)
5.8 Lines and Planes in Space (Section 12.5)
[Back to MATH 211]
The following is based on Thomas’ Calculus: Early Transcendentals, by Weir, Hass, and Thomas, 12th edition.
Module 1 Integration
1.1 Antiderivatives (Section 4.8)
1.2 Area and Estimating with Finite Sums (Section 5.1)
1.3 Sigma Notation and Limits of Finite Sums (Section 5.2)
1.4 The Definite Integral (Section 5.3)
1.5 The Fundamental Theorem of Calculus (Section 5.4)
1.6 The Substitution Method (Section 5.5)
1.7 Substitution and Area Between Curves (Section 5.6)
Module 2 Applications of Definite Integrals
2.1 Volumes Using Cross-Sections (Section 6.1)
2.2 Volumes Using Cylindrical Shells (Section 6.2)
2.3 Arc Length (Section 6.3)
2.4 Areas of Surfaces of Revolution (Section 6.4)
2.5 Work and Fluid Forces (Section 6.5)
2.6 Moments and Centers of Mass (Section 6.6)
Module 3 Techniques of Integration
3.1 The Logarithm as an Integral (Section 7.1)
3.2 Integration by Parts (Section 8.1)
3.3 Trigonometric Integrals (Section 8.2)
3.4 Trigonometric Substitutions (Section 8.3)
3.5 Integration of Rational Functions by Partial Fractions (Section 8.4)
3.6 Numerical Integration (Section 8.6)
3.7 Improper Integrals (Section 8.7)
Module 4 Series and Sequences
4.1 Sequences and Infinite Series (Sections 10.1, 10.2)
4.2 The Integral Test (Section 10.3)
4.3 Comparison Tests (Section 10.4)
4.4 The Ratio and Root Tests (Section 10.5)
4.5 Alternating Series, Absolute and Conditional Convergence (Section 10.6)
4.6 Power Series (Section 10.7)
4.7 Taylor and Maclaurin Series (Section 10.8)
4.8 Convergence of Taylor Series (Section 10.9)
4.9 Applications of Taylor Series (Section 10.10)
Module 5 Parametric Equations, Polar Coordinates and Vectors
5.1 Parametrizations of Plane Curves (Section 11.1)
5.2 Calculus with Parametric Curves (Section 11.2)
5.3 Polar Coordinates (Sections 11.3, 11.4)
5.4 Areas and Lengths in Polar Coordinates (Section 11.5)
5.5 Three-Dimensional Coordinate Systems and Vectors (Sections 12.1, 12.2)
5.6 The Dot Product (Section 12.3)
5.7 The Cross Product (Section 12.4)
5.8 Lines and Planes in Space (Section 12.5)