Presentation is loading. Please wait.

Presentation is loading. Please wait.

Copyright Kaplan AEC Education, 2008 Calculus and Differential Equations Outline Overview DIFFERENTIAL CALCULUS, p. 45 Definition of a Function Definition.

Published byChristine Richardson Modified over 8 years ago

Similar presentations

Presentation on theme: "Copyright Kaplan AEC Education, 2008 Calculus and Differential Equations Outline Overview DIFFERENTIAL CALCULUS, p. 45 Definition of a Function Definition."— Presentation transcript:

1 Copyright Kaplan AEC Education, 2008 Calculus and Differential Equations Outline Overview DIFFERENTIAL CALCULUS, p. 45 Definition of a Function Definition of a Derivative Some Relations Among Derivatives Table of Derivatives Slope of a Curve: Tangent and Normal

2 Copyright Kaplan AEC Education, 2008 Outline Overview Continued DIFFERENTIAL CALCULUS, p. 45 Maximum and Minimum Values of a Function Points of Inflection of a Curve Taylor and Maclaurin Series Evaluation of Indeterminate Forms Differential of a Function Functions of Several Variables, Partial Derivatives, and Differentials

3 Copyright Kaplan AEC Education, 2008 Outline Overview Continued INTEGRAL CALCULUS, p. 51 Definition of an Integral Fundamental Theorems on Integrals –Moment of Inertia –Center of Gravity –Work

4 Copyright Kaplan AEC Education, 2008 Outline Overview Continued DIFFERENTIAL EQUATIONS, p.53 Definitions Notation Equations of First Order and First Degree –Variables Separable –Linear Equation Second-Order Differential Equations

5 Copyright Kaplan AEC Education, 2008 Outline Overview Continued DIFFERENTIAL EQUATIONS, p. 53 Constant Coefficients –Variation of Parameters –Undetermined Coefficients Euler Equations Laplace Transform

6 Copyright Kaplan AEC Education, 2008 Basic Rules for Derivatives

7 Copyright Kaplan AEC Education, 2008 Solution

8 Copyright Kaplan AEC Education, 2008 The Chain Rule

9 Copyright Kaplan AEC Education, 2008 Solution

10 Copyright Kaplan AEC Education, 2008 Maximum & Minimum Values of a Function

11 Copyright Kaplan AEC Education, 2008 Solution

12 Copyright Kaplan AEC Education, 2008 Concavity & Points of Inflection

13 Copyright Kaplan AEC Education, 2008 Solution

14 Copyright Kaplan AEC Education, 2008 Solution (continued)

15 Copyright Kaplan AEC Education, 2008 Differential Equations with Variables Separable

16 Copyright Kaplan AEC Education, 2008 Solution

17 Copyright Kaplan AEC Education, 2008 Taylor Series

18 Copyright Kaplan AEC Education, 2008 Solution

19 Copyright Kaplan AEC Education, 2008 Maclaurin Series

20 Copyright Kaplan AEC Education, 2008 Solution

21 Copyright Kaplan AEC Education, 2008 Second Order Linear Equations

22 Copyright Kaplan AEC Education, 2008 Solution

23 Copyright Kaplan AEC Education, 2008 Solution (continued)

24 Copyright Kaplan AEC Education, 2008 Euler Equations

25 Copyright Kaplan AEC Education, 2008 Solution

26 Copyright Kaplan AEC Education, 2008 Method of Variation of Parameters

27 Copyright Kaplan AEC Education, 2008 Solution

28 Copyright Kaplan AEC Education, 2008 Laplace Transforms

29 Copyright Kaplan AEC Education, 2008 Solution

30 Copyright Kaplan AEC Education, 2008 Convolution

31 Copyright Kaplan AEC Education, 2008 Solution

Download ppt "Copyright Kaplan AEC Education, 2008 Calculus and Differential Equations Outline Overview DIFFERENTIAL CALCULUS, p. 45 Definition of a Function Definition."

Similar presentations

AP Exam Review (Chapter 2) Differentiability. AP Exam Review (Chapter 2) Product Rule.

AP Exam Review (Chapter 2) Differentiability. AP Exam Review (Chapter 2) Product Rule.
Created by Jason L. Bradbury State Standard – 15.0b Students use the fundamental theorem of calculus to interpret integrals as antidervivatives. – 14.0.

Created by Jason L. Bradbury State Standard – 15.0b Students use the fundamental theorem of calculus to interpret integrals as antidervivatives. – 14.0.
Unit 6 – Fundamentals of Calculus Section 6

Unit 6 – Fundamentals of Calculus Section 6
The Chain Rule Section 3.6c.

The Chain Rule Section 3.6c.
The Derivative and the Tangent Line Problem. Local Linearity.

The Derivative and the Tangent Line Problem. Local Linearity.
ESSENTIAL CALCULUS CH11 Partial derivatives

ESSENTIAL CALCULUS CH11 Partial derivatives
DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.

DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.
Derivatives - Equation of the Tangent Line Now that we can find the slope of the tangent line of a function at a given point, we need to find the equation.

Derivatives - Equation of the Tangent Line Now that we can find the slope of the tangent line of a function at a given point, we need to find the equation.
Chapter 2: Second-Order Differential Equations

Chapter 2: Second-Order Differential Equations
Jeopardy comments/answers April 2008. Existence Uniqueness Each kind of differential equation we studied had a corresponding existence and uniqueness.

Jeopardy comments/answers April Existence Uniqueness Each kind of differential equation we studied had a corresponding existence and uniqueness.
Ch 5.1: Review of Power Series Finding the general solution of a linear differential equation depends on determining a fundamental set of solutions of.

Ch 5.1: Review of Power Series Finding the general solution of a linear differential equation depends on determining a fundamental set of solutions of.
Ordinary Differential Equations Final Review Shurong Sun University of Jinan Semester 1, 2011-2012.

Ordinary Differential Equations Final Review Shurong Sun University of Jinan Semester 1,
1 Part 1: Ordinary Differential Equations Ch1: First-Order Differential Equations Ch2: Second-Order Differential Equations Ch3: The Laplace Transform Ch4:

1 Part 1: Ordinary Differential Equations Ch1: First-Order Differential Equations Ch2: Second-Order Differential Equations Ch3: The Laplace Transform Ch4:
Section 6.1: Euler’s Method. Local Linearity and Differential Equations Slope at (2,0): Tangent line at (2,0): Not a good approximation. Consider smaller.

Section 6.1: Euler’s Method. Local Linearity and Differential Equations Slope at (2,0): Tangent line at (2,0): Not a good approximation. Consider smaller.
First Order Linear Equations Integrating Factors.

First Order Linear Equations Integrating Factors.
(MTH 250) Lecture 24 Calculus. Previous Lecture’s Summary Multivariable functions Limits along smooth curves Limits of multivariable functions Continuity.

(MTH 250) Lecture 24 Calculus. Previous Lecture’s Summary Multivariable functions Limits along smooth curves Limits of multivariable functions Continuity.
ORDINARY DIFFERENTIAL EQUATION (ODE) LAPLACE TRANSFORM.

ORDINARY DIFFERENTIAL EQUATION (ODE) LAPLACE TRANSFORM.
S C alculu. 1. Preliminaries 2. Functions and Limits 3. The Derivative 4. Applications of the Derivative 5. The Integral 6. Applications of the Integral.

S C alculu. 1. Preliminaries 2. Functions and Limits 3. The Derivative 4. Applications of the Derivative 5. The Integral 6. Applications of the Integral.
5.4 The Fundamental Theorem. The Fundamental Theorem of Calculus, Part 1 If f is continuous on, then the function has a derivative at every point in,

5.4 The Fundamental Theorem. The Fundamental Theorem of Calculus, Part 1 If f is continuous on, then the function has a derivative at every point in,
Fundamental Theorems of Calculus 6.4. The First (second?) Fundamental Theorem of Calculus If f is continuous on, then the function has a derivative at.

Fundamental Theorems of Calculus 6.4. The First (second?) Fundamental Theorem of Calculus If f is continuous on, then the function has a derivative at.

Similar presentations

Ads by Google