MATH 241: Calculus and Analytic Geometry II
Tentative Course Outline
| Topics | |
Reading(*) | |
Assignments | |
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Inverse Functions
- Inverse Functions
- Exponential Functions and their Derivatives
- Logarithmic Functions
- Derivatives of Logarithmic Functions
- Exponential Growth and Decay
- Inverse Trigonometric Functions
- Hyperbolic Functions
- Indeterminate Forms and l'Hospital's Rule
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Chapter 6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
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Techniques of Integration
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitution
- Integration of Rational Functions
- Strategy of Integration
- Improper Integrals
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Chapter 7
7.1
7.2
7.3
7.4
7.5
7.8
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***** Midterm Exam I ***** |
Further Application of Integration
- Arc Length
- Area of Surface of Revolution
- Application to Physics and Engineering
- Applications to Biology
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Chapter 8
8.1
8.2
8.3
8.4 |
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Parametric Equations and Polar
Coordinates
- Curves Defined by Parametric Equations
- Calculus with Parametric Curves
- Polar Coordinates
- Areas and Lengths in Polar Coordinates
- Conic Sections
- Conic Sections in Polar Coordinates
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Chapter 10
10.1
10.2
10.3
10.4
10.5
10.6 |
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***** Midterm Exam II ***** |
Infinite Sequences and Series
- Sequences
- Series
- The Integral Test and Estimates of Sums
- The Comparison Tests
- Alternating Series
- Absolute Convergence, Ratio and Root Tests
- Strategy for Testing Series
- Power Series
- Representations of Functions as Power Series
- Taylor and Maclaurin Series
- Applications of Taylor Polynomials
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Chapter 11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11 |
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***** Final Exam ***** |
(*)
Chapter numbers correspond to the 7th Edition of the Textbook.