| 1. | |
Differentiation Rules | This section presents the definition of the derivative, derivatives of the trigonometric functions, derivatives of product and quotient functions. Further, Chain Rule and implicit differentiation are given. |  |
| 2. | |
Applications of Differentiation | This section is devoted to the derivatives of inverse trig functions, derivatives of the exponential and logarithm functions. | |
| 3. | |
Integrals | This section starts with the area and distance problems. Also, definite integrals and its properties are presented. Evaluation of definite integral and Fundamental Theorem of Calculus are given. | |
| 4. | |
Integration by Parts | Partial fractions are used to evaluate integrals involving some rational functions. Integrals with infinite intervals of integration and integrals with discontinuous integrands are presented. | |
| 5. | |
Applications of Integration | This section starts with the area and distance problems. Also, definite integrals and its properties are presented. Evaluation of definite integral and Fundamental Theorem of Calculus are given. | |
| 6. | |
Arc Length | This section deals how to determine the length of a curve. Also, integrals used to determine the average value of a function. Further, this section is devoted to finding the volume of a solid of revolution. | |
| 7. | |
Applications to Physics and Engineering | In this section, some application of derivatives to physics and engineering is given. Further, probability density functions and computing the mean of a probability density function is presented. | |
| 8. | |
Infinite Sequences and Series | This section contains sequences and series. Basic terminology and convergence of sequences are given. Further, basics of infinite series are discussed. Using the Integral Test, Comparison Test and the Alternating Series Test to determine if a series converges or diverges are being discussed. | |
| 9. | |
Power Series | In this section, we have discussed about how to find a power series representation of a function, Taylor and Maclaurin Series for a function. Further, couple of applications of series are given. | |
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