Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The...

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Transcript of Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The...

Page 1: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 2: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 3: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 4: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 5: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 6: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 7: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 8: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 9: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily
Page 10: Chapter 7 Differential Equations and Mathematical Modeling Leibniz Notation and Antiderivatives The appearance of the differential "dx" in the definite integral f (x) dx is easily

13.1 Antiderivatives and Indefinite Integrals · INDEFINITE INTEGRALS f(x)dx. Indefinite Integral Formulas and Properties . The indefinite integral of a function ( ) is the family

13.1 Antiderivatives and Indefinite Integrals · INDEFINITE INTEGRALS f(x)dx. Indefinite Integral Formulas and Properties . The indefinite integral of a function ( ) is the family

DIFFERENTIAL EQUATIONS · 2019. 3. 15. · DIFFERENTIAL EQUATIONS 181 dy dx = 2Ae2x – 2 B.e–2x and 2 2 d y dx = 4Ae2x + 4Be–2x Thus 2 2 d y dx = 4y i.e., 2 2 d y dx – 4y =

DIFFERENTIAL EQUATIONS · 2019. 3. 15. · DIFFERENTIAL EQUATIONS 181 dy dx = 2Ae2x – 2 B.e–2x and 2 2 d y dx = 4Ae2x + 4Be–2x Thus 2 2 d y dx = 4y i.e., 2 2 d y dx – 4y =

DIFFERENTIAL EQUATIONS...DIFFERENTIAL EQUATIONS 181 dy dx = 2Ae2x – 2 B.e–2x and 2 2 d y dx = 4Ae2x + 4Be–2x Thus 2 2 d y dx = 4y i.e., 2 2 d y dx – 4y = 0. Example 2 Find

DIFFERENTIAL EQUATIONS...DIFFERENTIAL EQUATIONS 181 dy dx = 2Ae2x – 2 B.e–2x and 2 2 d y dx = 4Ae2x + 4Be–2x Thus 2 2 d y dx = 4y i.e., 2 2 d y dx – 4y = 0. Example 2 Find

Lesson 23: Antiderivatives (slides)

Lesson 23: Antiderivatives (slides)

Antiderivatives anoyrnd Slope Fields

Antiderivatives anoyrnd Slope Fields

The Finite‐Difference Method · Differential Equation to Solve Conventional FDM (1 of 3) Slide 20 Step 1 –Start with a differential equation to be solved. 2 2 df df abfc dx dx

The Finite‐Difference Method · Differential Equation to Solve Conventional FDM (1 of 3) Slide 20 Step 1 –Start with a differential equation to be solved. 2 2 df df abfc dx dx

and 6-4 Slope …  · Web viewAP Calculus ABName_____ 6.1 and 6.4 Slope Fields & Separable Differential Equations. I can construct antiderivatives using the FTC

and 6-4 Slope …  · Web viewAP Calculus ABName_____ 6.1 and 6.4 Slope Fields & Separable Differential Equations. I can construct antiderivatives using the FTC

Antiderivatives (7.4, 8.2, 10.1)

Antiderivatives (7.4, 8.2, 10.1)

Antiderivatives and Initial Value Problems - Dartmouth … · Antiderivatives and Initial Value Problems Warm up If d dx f (x) ... “Solve the di↵erential equation d dx y = x2.”

Antiderivatives and Initial Value Problems - Dartmouth … · Antiderivatives and Initial Value Problems Warm up If d dx f (x) ... “Solve the di↵erential equation d dx y = x2.”

Differential EquationsThe order of the differential equation 2 2 2 23 0 dy dy xy dx dx − += is (A) 2 (B) 1 (C) 0 (D) not defined 9.3. General and Particular Solutions of a Differential

Differential EquationsThe order of the differential equation 2 2 2 23 0 dy dy xy dx dx − += is (A) 2 (B) 1 (C) 0 (D) not defined 9.3. General and Particular Solutions of a Differential

ANTIDERIVATIVES AND INDEFINITE INTEGRATION

ANTIDERIVATIVES AND INDEFINITE INTEGRATION

Lesson 21: Antiderivatives (slides)

Lesson 21: Antiderivatives (slides)

Antiderivatives - Department of Mathematics | UConn

Antiderivatives - Department of Mathematics | UConn

6.1 Antiderivatives and Indefinite Integration

6.1 Antiderivatives and Indefinite Integration

Section 4.9 Antiderivatives

Section 4.9 Antiderivatives

Section 4.8 - Antiderivatives

Section 4.8 - Antiderivatives

Ordinary Differential Equations - Numerical FactoryOrdinary Differential Equations • Analytical Solution: (only in few cases) • Separate variables: dy dx x dy x dx y x C ³ ³

Ordinary Differential Equations - Numerical FactoryOrdinary Differential Equations • Analytical Solution: (only in few cases) • Separate variables: dy dx x dy x dx y x C ³ ³

Lecture 18 antiderivatives - section 4.8

Lecture 18 antiderivatives - section 4.8

Derivatives, Antiderivatives, and Indefinite Integrals

Derivatives, Antiderivatives, and Indefinite Integrals

7) Calculating Antiderivatives

7) Calculating Antiderivatives