Calculus-1

Lecture notes 2011 spring semester

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2.2 The limit of a Function

2.3 Calculating Limits Using the Limit Law

2.4 Continuity

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6.1 More About Areas

6.2 Volumes

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2.5 Limit Involving Infinity

2.6 Derivatives and Rates of change

2.7 The Derivatives as a Function

2.8 what does  f' say about f?

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6.3 Volumes by Cylindrical Shells

6.4 Arc Length

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3.1 Derivatives of Polynomials and Exponential Function

3.2 The Product and Quotient Rules

3.3 Derivatives of Trigonometric Function

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6.5 Average Values of a Function

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3.3 Derivatives of Trigonometric Function

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7.1 Modeling with Differential Equations

7.2 Direction Fields and Euler's Method

7.3 Separable Equations

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3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Inverse Trigonometric functions and Their derivatives

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7.4 Exponential Growth and Decay

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3.5 Implicit Differentiation

3.6 Inverse Trigonometric functions and Their derivatives

3.7 Derivatives of Logarithmic Function

3.8 Rates of Change in the Natural and Social Sciences

3.9 Linear Approximations and Differentials

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7.5 The Logic Equations

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4.1 Related Rates

4.2 Maximum and Minimum Values

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7.5 The Logic Equations

7.6 Predator-Prey Systems

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4.3 Derivatives and the Shapes of curves

4.5 Indeterminate Forms and l'Hospital's Rule

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8.1 Sequences

8.2 Series

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4.6 Optimization Problems

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8.3 The Integral and Comprison Tests; Estimation Sums

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5.1 Areas and Distances

5.2 The Definite Integrals

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8.4 Other Convergence Tests

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5.3 Evaluating Definite integrals

5.4 The Fundamental Theorem of Calculus

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8.4 Other Convergence Tests

8.5 Power Series

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5.4 The Fundamental Theorem of Calculus

5.5 The substitution Rule

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8.6 Representations of Functions as Power Series

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5.6 Integration by Part

5.7 Additional Techniques of Integration

5.10 Improper integrals

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8.7 Taylor and Maclaurin Series