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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

+Mid-term Exam +Final Exam