Midterm
1. Mathematical induction
- Number systems and elementary functions
- Mathematical induction
2. Limits and Continuity
- Limits (An Intuitive Approach)
- Computing Limits - Limits at Infinity
- Limits of Trigonometric Functions
- Continuity
3. Differentiation
- Tangent Lines and Rates of Change
- The Derivative - Techniques of Differentiation
- Derivatives of Trigonometric Functions
- The Chain Rule - Implicit Differentiation
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Logarithmic and Exponential Functions
- Derivatives of Hyperbolic Functions
- Higher Derivatives
- Linear Approximations
4. Applications of Differentiation
- Related Rates
- L’Hopital’s Rule; Indeterminate Forms
- Intervals of Increase and Decrease; Concavity
- Relative Extrema; First and Second Derivative Tests
- Graphs of Polynomials and Rational Functions
- Maximum and Minimum Values of a Function
- Applied Maximum and Minimum Problems
- Rolle’s Theorem; Mean Value Theorem
5. Integration
- Antiderivatives; The Indefinite Integral
- Integration by Substitution
- The Definite Integral
- The Fundamental Theorem of Calculus
1. Mathematical induction
- Number systems and elementary functions
- Mathematical induction
2. Limits and Continuity
- Limits (An Intuitive Approach)
- Computing Limits - Limits at Infinity
- Limits of Trigonometric Functions
- Continuity
3. Differentiation
- Tangent Lines and Rates of Change
- The Derivative - Techniques of Differentiation
- Derivatives of Trigonometric Functions
- The Chain Rule - Implicit Differentiation
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Logarithmic and Exponential Functions
- Derivatives of Hyperbolic Functions
- Higher Derivatives
- Linear Approximations
4. Applications of Differentiation
- Related Rates
- L’Hopital’s Rule; Indeterminate Forms
- Intervals of Increase and Decrease; Concavity
- Relative Extrema; First and Second Derivative Tests
- Graphs of Polynomials and Rational Functions
- Maximum and Minimum Values of a Function
- Applied Maximum and Minimum Problems
- Rolle’s Theorem; Mean Value Theorem
5. Integration
- Antiderivatives; The Indefinite Integral
- Integration by Substitution
- The Definite Integral
- The Fundamental Theorem of Calculus
6. Applications of Definite Integral
- Area Between Two Curves
- Volumes by Slicing; Disks and Washers
- Volumes by Cylindrical Shells
- Length of a Plane Curve
7. Techniques of Integration
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitutions
- Integrating Rational Functions by Partial Fractions
- Numerical Integration
- Improper Integrals
8. Infinite Series
- Sequence
- Infinite Series
- Convergence Tests
- Taylor’s Theorem for Basic Functions
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