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- https://math.libretexts.org/Courses/Santiago_Canyon_College
- https://math.libretexts.org/Courses/Mount_Royal_University/MATH_3200%3A_Mathematical_MethodsMathematical Methods provides an introduction to vector calculus, ordinary differential equations, and partial differential equations including a variety of applications. Topics include: optimization,...Mathematical Methods provides an introduction to vector calculus, ordinary differential equations, and partial differential equations including a variety of applications. Topics include: optimization, line and surface integrals, Green’s theorem, Stokes’ theorem, the Divergence theorem, and the theory of systems of linear differential equations.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)
- https://math.libretexts.org/Courses/Highline_College/MATH_141%3A_Precalculus_I_(2nd_Edition)This course includes, but not limited to piece-wise, composite, inverse, polynomial, rational, exponential, and logarithmic functions. Also discussed are properties of functions, their relationship to...This course includes, but not limited to piece-wise, composite, inverse, polynomial, rational, exponential, and logarithmic functions. Also discussed are properties of functions, their relationship to equations and inequalities, as well as applications, and circles.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_400%3A_Calculus_I_-_Differential_Calculus/03%3A_Discovering_Derivatives/3.01%3A_Derivatives_of_Polynomial_FunctionsThis section covers how to find the derivatives of polynomial functions. It introduces the basic power rule for differentiation and demonstrates how to apply it to terms of various degrees. The sectio...This section covers how to find the derivatives of polynomial functions. It introduces the basic power rule for differentiation and demonstrates how to apply it to terms of various degrees. The section includes examples of differentiating polynomials and highlights the key steps for finding first and higher-order derivatives of polynomial functions. The focus is on understanding the straightforward process of differentiating terms of the form xn.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/10%3A_Parametric_Equations_and_Polar_Coordinates/10.03%3A_Calculus_of_Parametric_CurvesThis section covers the calculus of parametric curves, including finding derivatives and integrals for curves defined parametrically. It explains how to compute the slope of the tangent line, arc leng...This section covers the calculus of parametric curves, including finding derivatives and integrals for curves defined parametrically. It explains how to compute the slope of the tangent line, arc length, and area under a parametric curve. Examples demonstrate how to apply these techniques to analyze the geometric and physical properties of parametric equations.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/08%3A_Sequences_and_Series/8.05%3A_The_Comparison_TestsThis section explains the Direct and Limit Comparison Tests for determining the convergence or divergence of series. The Direct Comparison Test involves comparing terms with a known series, while the ...This section explains the Direct and Limit Comparison Tests for determining the convergence or divergence of series. The Direct Comparison Test involves comparing terms with a known series, while the Limit Comparison Test uses the limit of the ratio between terms of two series. Examples illustrate how to apply these tests effectively to assess series convergence.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/07%3A_Techniques_of_Integration/7.01%3A_Expanding_the_Substitution_MethodThis section covers techniques for integrating trigonometric functions, focusing on integrals involving powers of sine, cosine, secant, and tangent. It explores strategies such as using trigonometric ...This section covers techniques for integrating trigonometric functions, focusing on integrals involving powers of sine, cosine, secant, and tangent. It explores strategies such as using trigonometric identities to simplify integrals and applying substitution when necessary. The section provides examples to illustrate different cases, helping to build a deeper understanding of how to handle integrals of trigonometric functions effectively.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/05%3A_Investigating_Integrals/5.01%3A_Antiderivatives_and_Indefinite_IntegralsThis section introduces antiderivatives and indefinite integrals, explaining the process of reversing differentiation to find the original function. It covers basic integration rules, notation, and th...This section introduces antiderivatives and indefinite integrals, explaining the process of reversing differentiation to find the original function. It covers basic integration rules, notation, and the concept of the constant of integration. Examples demonstrate finding antiderivatives for various functions, establishing foundational skills for solving integral problems.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/03%3A_Discovering_Derivatives/3.05%3A_Derivatives_of_Exponential_and_Hyperbolic_FunctionsThis section covers the differentiation of exponential and hyperbolic functions. It explains how to find derivatives of exponential functions, focusing on base e, and explores the rules for differ...This section covers the differentiation of exponential and hyperbolic functions. It explains how to find derivatives of exponential functions, focusing on base e, and explores the rules for differentiating hyperbolic functions like sinh, cosh, and others. The section provides examples to apply these differentiation techniques to various types of functions and shows their connections to real-world applications.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/05%3A_Investigating_Integrals/5.06%3A_Integration_by_SubstitutionThis section introduces integration by substitution, a method used to simplify integrals by making a substitution that transforms the integral into a more manageable form. It explains how to identify ...This section introduces integration by substitution, a method used to simplify integrals by making a substitution that transforms the integral into a more manageable form. It explains how to identify the substitution, change variables, and adjust the limits of integration for definite integrals. Examples illustrate its application to a variety of functions, highlighting its role as the reverse process of the chain rule in differentiation.
