Math 113 (Administration)

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0. Prerequisites
   1. Intervals, Inequalities, and Absolute Values (Appendix F and G)
   2. Lines and Circles (Appendix H and I)
   3. Functions, their Notation and Graphs (Appendix B, C, D)

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1. Functions (Review)
   1. Functions, their Notation, and Graphs (Appendix B, C, D)
   2. Composition and Inverses (Appendices D, E, 1.7)
   3. Exponentials and Logarithms (1.8)
   4. Trigonometric Functions and their Inverses (Appendix A, 0.4)
2. Limits and Graphs
   1. Limits (1.1, 1.2, 1.3)
   2. Continuity (1.5, 1.6)
   3. Graphs and Asymptotes (Appendices B and C, 1.5)
   4. Formal Definition and $\epsilon$-$\delta$ Proofs*
3. Differentiation
   1. Tangent Lines and Rates of Change (2.1, 2.2)
   2. Calculating Derivatives by Definition (2.1, 2.2)
   3. Differentiation Rules (2.3, 2.4, 2.5, 2.6, 3.2, 3.3)
      1. Sum Rule
      2. Product Rule
      3. Quotient Rule
      4. Power Rule
      5. Chain Rule
      6. Trigonometric Rules
      7. Exponential and Log Rules
      8. Inverse Trigonometric Rules
   4. Implicit Differentiation (3.1)
   5. Logarithmic Differentiation* (3.2)
   6. Taylor Polynomial Approximations and Maclaurin Series (9.7, 9.8)
4. Applications of Differentiation
   1. Related Rates Problems (3.4)
   2. Optimization Problems (4.5)
   3. Analysis of Functions
      1. Increasing, Decreasing, Concavity (4.1)
      2. Reletive Extrema and Graphs (4.2)
      3. Rational Functions, Cusps, and Vertical Tangents (4.3)
      4. Absolute Maximum and Minimum (4.4)
5. Integration
   1. Calculating Definite Integrals by Definition (5.4, 5.5)
   2. The Fundamental Theorem of Calculus (5.6)
   3. Integration by Substitution (5.3, 5.9)
   4. Integration by Parts (5.6)
   5. Improper Integrals (7.8)
   6. Partial Fractions* (7.5)
   7. Trigonometric Substitutions* (7.3, 7.4)
6. Applications of Integration
   1. Area Between Curves (6.1)
   2. Volumes of Solids of Revolution (6.2)
   3. Surface Area (6.5)
   4. Arc Length* (6.4)

See the course calendar for details concerning exams and quizzes.

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^* Time permitting.

Math 113 (Fall 2022) web pages Created: 02 Sep 2022 Last modified: 11 Nov 2022 at 5:05 PM Comments to: dpvc@union.edu

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