math 151 (MATH151)

Notes taken on the topic of rates of change in the natural and social sciences as taught by Amy Austin in MATH 151 at TAMU. These notes contain definitions and examples of how rates of change are applied to the natural and social sciences.

Notes taken on the topic of optimization problems as taught by Amy Austin in MATH 151 at TAMU. These notes contain multiple word problem examples with formulas and detailed work for using calculus to find the optimized values in a specific situation.

Notes taken on the topic of exponential growth and decay as taught by Amy Austin in MATH 151 at TAMU. These notes contain examples of how to solve exponential growth and decay problems as well as how to use Newton's Rate of Cooling equation.

Notes taken on the topic of related rates as taught by Amy Austin in MATH 151 at TAMU. These notes contain numerous real-world examples as well as formulas and expressions used to solve problems on related rates.

Notes taken on the topic of antiderivatives as taught by Amy Austin in MATH 151 at TAMU. These notes contain formulas and definitions for antiderivatives (integrals) and shortcuts for them from certain functions such as x^n, e^x, a^x, and so on. There are also numerous examples showing work for these formulas and shortcuts as well as a couple of real-world examples.

Notes taken on the topic of areas and distances as taught by Amy Austin in MATH 151 at TAMU. These notes contain definitions and formulas for estimating areas and distances under curves using the Riemann sum method. They also contain numerous examples showing this work and diagramming.

Notes taken on the topic of the definite integral as taught by Amy Austin in MATH 151 at TAMU. These notes contain definitions for how to solve definite integrals, as well as numerous examples with work and diagrams supporting the definitions.

Notes taken on the topic of the fundamental theorem of calculus as taught by Amy Austin in MATH 151 at TAMU. These notes contain a definition of the fundamental theorem of calculus, which is the basis for understanding integrals. They then go on to show work for numerous examples of using this definition.

Notes taken on the topic of indefinite integrals and the net change theorem as taught by Amy Austin in MATH 151 at TAMU. These notes contain many examples of how to calculate indefinite integrals and how to use the net change theorem. The examples include natural logs, trigonometric functions, and inverse trigonometric functions as well.

Notes taken on the topic of linear approximations and differentials as taught by Amy Austin in MATH 151 at TAMU. These notes contain formulas and explanations for how to perform linear approximations and differentials. They also contains lots of examples showing how to use these formulas.