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 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 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 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.

Notes taken on the topic of maximum and minimum values as taught by Amy Austin in MATH 151 at TAMU. These notes contain definitions, tips, and formulas to find the absolute and local maximum and minimum values for a function. There are then multiple examples describing and showing these processes. Finally, the notes have a definition of the extreme value theorem and examples showing this as well.

Notes taken on the topic of the mean value theorem as taught by Amy Austin in MATH 151 at TAMU. These notes contain definitions and explanations of the mean value theorem as well as Rolle's theorem. They then go into detail and provide multiple examples and work for each theorem.

Notes taken on the topic of derivatives and shapes of curves as taught by Amy Austin in MATH 151 at TAMU. These notes contain shortcuts and examples to describe the motion of curves as they relate to their derivatives and double derivatives.

Notes taken on the topic of L'Hopital's rule as taught by Amy Austin in MATH 151 at TAMU. These notes contain numerous examples of how and when to use L'Hopital's Rule in many circumstances such as all of the indeterminate forms including products, differences, and powers.

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.