math 151 (MATH151)

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 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 written on the topic of inverse trigonometric functions as taught by Amy Austin in MATH 151 at TAMU. These notes contain definitions, properties, and examples of the inverse trigonometric functions.

Notes written on the topic of continuity as taught by Amy Austin in MATH 151 at TAMU. These notes contain the definition of continuity and various examples of how to find the continuity of a function. The intermediate value theorem is also present, all summing to provide a basis of terms and understandings for derivatives.

Notes written on the topic of tangents, velocities, and other rates of change as taught by Amy Austin in MATH 151 at TAMU. These notes contain examples and definitions of tangents, velocities, and other rates of change as a precursor to the introduction of derivatives.

Notes written on the topic of explaining derivatives as a function as taught by Amy Austin in MATH 151 at TAMU. These notes contain the definition and interpretations of derivatives as explained in their basic terms, including the formula for a derivative described as a limit and other examples.

Notes written on the topic of product and quotient rules as taught by Amy Austin in MATH 151 at TAMU. These notes contain multiple examples of the product and quotient rules for derivatives.

Notes written on the topic of derivatives of trig functions as taught by Amy Austin in MATH 151 at TAMU. These notes contain formulas, examples, and work for the derivatives of trigonometric functions.