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18.1.1: Introduction to Exponential Functions
https://math.libretexts.org/Bookshelves/Applied_Mathematics/Developmental_Math_(NROC)/18%3A_Exponential_and_Logarithmic_Functions/18.01%3A_Exponential_Functions/18.1.01%3A_Introduction_to_Exponential_Functions
For example, the compound interest formula is $A=P\left(1+\frac{r}{m}\right)^{m t}$ , where $P$ is the principal (the initial investment that is gathering interest) and $A$ is the amount of money...For example, the compound interest formula is $A=P\left(1+\frac{r}{m}\right)^{m t}$ , where $P$ is the principal (the initial investment that is gathering interest) and $A$ is the amount of money you would have, with interest, at the end of $t$ years, using an annual interest rate of $r$ (expressed as a decimal) and $m$ compounding periods per year.
3.4: Constant coefficient second order linear ODEs
https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.04%3A_Constant_coefficient_second_order_linear_ODEs
This page explains solving second-order linear homogeneous differential equations using the characteristic equation method, covering distinct, repeated, and complex roots. It includes the general solu...This page explains solving second-order linear homogeneous differential equations using the characteristic equation method, covering distinct, repeated, and complex roots. It includes the general solution forms and adaptations for double roots, along with examples. Additionally, it discusses complex numbers, their properties, and Euler's formula, applying these concepts to derive trigonometric identities.
3.1: Integration by Parts
https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.01%3A_Integration_by_Parts
This page provides an overview of integration by parts, a technique used to simplify the integration of products of functions. It includes the formula derived from the product rule, guidance on choosi...This page provides an overview of integration by parts, a technique used to simplify the integration of products of functions. It includes the formula derived from the product rule, guidance on choosing functions with the LIATE mnemonic, and multiple examples ranging from logarithmic to trigonometric integrals. The text also discusses evaluating both definite and indefinite integrals and emphasizes validating results through differentiation.
2: Applications of Integration
https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration
In this chapter, we use definite integrals to calculate the force exerted on the dam when the reservoir is full and we examine how changing water levels affect that force. Hydrostatic force is only on...In this chapter, we use definite integrals to calculate the force exerted on the dam when the reservoir is full and we examine how changing water levels affect that force. Hydrostatic force is only one of the many applications of definite integrals we explore in this chapter. From geometric applications such as surface area, and volume to physical applications such as mass and work, to growth and decay models, definite integrals are a powerful tool to help us understand and model the world aroun
2.7: Integrals, Exponential Functions, and Logarithms
https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/02%3A_Applications_of_Integration/2.07%3A_Integrals_Exponential_Functions_and_Logarithms
We already examined exponential functions and logarithms in earlier chapters. However, we glossed over some key details in the previous discussions. For example, we did not study how to treat exponent...We already examined exponential functions and logarithms in earlier chapters. However, we glossed over some key details in the previous discussions. For example, we did not study how to treat exponential functions with exponents that are irrational. The definition of the number e is another area where the previous development was somewhat incomplete. We now have the tools to deal with these concepts in a more mathematically rigorous way, and we do so in this section.
3.1E: Exercises for Section 3.1
https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/03%3A_Techniques_of_Integration/3.01%3A_Integration_by_Parts/3.1E%3A_Exercises_for_Section_3.1
This page provides exercises focusing on integration techniques, particularly integration by parts and basic methods. It presents specific integrals, suggested $u$ choices, and solved straightforwar...This page provides exercises focusing on integration techniques, particularly integration by parts and basic methods. It presents specific integrals, suggested $u$ choices, and solved straightforward integrals, including definite integrals with exact solutions. Also covered are problems involving areas and volumes from revolving curves and evaluating integrals with exponential, logarithmic, and trigonometric functions, alongside reduction formulas.
6: Appendices
https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/06%3A_Appendices
Contributors and Attributions Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download fo...Contributors and Attributions Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.
3.2E: Exercises for Section 3.2
https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/03%3A_Higher_order_linear_ODEs/3.02%3A_The_Method_of_Undetermined_Coefficients_I/3.2E%3A_Exercises_for_Section_3.2
This page provides exercises on finding particular solutions to differential equations, focusing on equations like $y''+by'+cy=f(x)$ . It covers general solutions, initial value problems, and superpo...This page provides exercises on finding particular solutions to differential equations, focusing on equations like $y''+by'+cy=f(x)$ . It covers general solutions, initial value problems, and superposition principles with various methods such as polynomials and exponentials. Additionally, it introduces techniques for integrating expressions like $\int e^{\alpha x}P(x)dx$ by transforming them for easier evaluation.

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