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Fundamentals of Engineering Calculus, Differential ...

Fundamentals of EngineeringCalculus, Differential equations & Transforms, andNumerical AnalysisBrody Dylan JohnsonSt. Louis UniversityBrody Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis1 / 30 OverviewOverviewAgenda:Problem solving with Just-In-Time lectures (50 minutes)Group work with more problems (30 minutes)Quiz (30 minutes)Topics:Calculus: Differential Calculus, Integral Calculus, Centroids andMoments of Inertia, Vector equations and Transforms: Differential equations , FourierSeries, laplace Transforms, Euler s ApproximationNumerical Analysis: Root Solving with Bisection Method and Newton : Many problems are taken from the Hughes-Hallett,Gleason, McCallum, et al.

Differential Equations and Transforms: Differential Equations, Fourier Series, Laplace Transforms, Euler’s Approximation Numerical Analysis: Root Solving with Bisection Method and Newton’s Method. Acknowledgement: Many problems are taken from the Hughes-Hallett, Gleason, McCallum, et al. Calculus textbook.

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1 Fundamentals of EngineeringCalculus, Differential equations & Transforms, andNumerical AnalysisBrody Dylan JohnsonSt. Louis UniversityBrody Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis1 / 30 OverviewOverviewAgenda:Problem solving with Just-In-Time lectures (50 minutes)Group work with more problems (30 minutes)Quiz (30 minutes)Topics:Calculus: Differential Calculus, Integral Calculus, Centroids andMoments of Inertia, Vector equations and Transforms: Differential equations , FourierSeries, laplace Transforms, Euler s ApproximationNumerical Analysis: Root Solving with Bisection Method and Newton : Many problems are taken from the Hughes-Hallett,Gleason, McCallum, et al.

2 Calculus Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis2 / 30 OverviewOverviewAgenda:Problem solving with Just-In-Time lectures (50 minutes)Group work with more problems (30 minutes)Quiz (30 minutes)Topics:Calculus: Differential Calculus, Integral Calculus, Centroids andMoments of Inertia, Vector equations and Transforms: Differential equations , FourierSeries, laplace Transforms, Euler s ApproximationNumerical Analysis: Root Solving with Bisection Method and Newton : Many problems are taken from the Hughes-Hallett,Gleason, McCallum, et al. Calculus Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis2 / 30 OverviewOverviewAgenda:Problem solving with Just-In-Time lectures (50 minutes)Group work with more problems (30 minutes)Quiz (30 minutes)Topics:Calculus: Differential Calculus, Integral Calculus, Centroids andMoments of Inertia, Vector equations and Transforms: Differential equations , FourierSeries, laplace Transforms, Euler s ApproximationNumerical Analysis: Root Solving with Bisection Method and Newton : Many problems are taken from the Hughes-Hallett,Gleason, McCallum, et al.

3 Calculus Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis2 / 30 OverviewOverviewAgenda:Problem solving with Just-In-Time lectures (50 minutes)Group work with more problems (30 minutes)Quiz (30 minutes)Topics:Calculus: Differential Calculus, Integral Calculus, Centroids andMoments of Inertia, Vector equations and Transforms: Differential equations , FourierSeries, laplace Transforms, Euler s ApproximationNumerical Analysis: Root Solving with Bisection Method and Newton : Many problems are taken from the Hughes-Hallett,Gleason, McCallum, et al. Calculus Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis2 / 30 OverviewOverviewAgenda:Problem solving with Just-In-Time lectures (50 minutes)Group work with more problems (30 minutes)Quiz (30 minutes)Topics:Calculus: Differential Calculus, Integral Calculus, Centroids andMoments of Inertia, Vector equations and Transforms: Differential equations , FourierSeries, laplace Transforms, Euler s ApproximationNumerical Analysis: Root Solving with Bisection Method and Newton : Many problems are taken from the Hughes-Hallett,Gleason, McCallum, et al.

4 Calculus Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis2 / 30 OverviewOverviewAgenda:Problem solving with Just-In-Time lectures (50 minutes)Group work with more problems (30 minutes)Quiz (30 minutes)Topics:Calculus: Differential Calculus, Integral Calculus, Centroids andMoments of Inertia, Vector equations and Transforms: Differential equations , FourierSeries, laplace Transforms, Euler s ApproximationNumerical Analysis: Root Solving with Bisection Method and Newton : Many problems are taken from the Hughes-Hallett,Gleason, McCallum, et al. Calculus Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis2 / 30 OverviewOverviewAgenda:Problem solving with Just-In-Time lectures (50 minutes)Group work with more problems (30 minutes)Quiz (30 minutes)Topics:Calculus: Differential Calculus, Integral Calculus, Centroids andMoments of Inertia, Vector equations and Transforms: Differential equations , FourierSeries, laplace Transforms, Euler s ApproximationNumerical Analysis: Root Solving with Bisection Method and Newton : Many problems are taken from the Hughes-Hallett,Gleason, McCallum, et al.

5 Calculus Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis2 / 30 CalculusDifferential CalculusProblem 1: Find the maximum and minimum values off(x) =x3 3x2+20on[ 1,3].Solution:Check endpoints and critical points (f (x) =0).f (x) =3x2 6x,f (x) =0= x=0, (x) =6x 6,f (0)<0 concave down; local max,f (2)>0 concave up; local values:f( 1) =16,f(0) =20,f(2) =16,f(3) = :f(x) =16 atx= 1 orx= :f(x) =20 atx=0 orx= Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis3 / 30 CalculusDifferential CalculusProblem 1: Find the maximum and minimum values off(x) =x3 3x2+20on[ 1,3].

6 Solution:Check endpoints and critical points (f (x) =0).f (x) =3x2 6x,f (x) =0= x=0, (x) =6x 6,f (0)<0 concave down; local max,f (2)>0 concave up; local values:f( 1) =16,f(0) =20,f(2) =16,f(3) = :f(x) =16 atx= 1 orx= :f(x) =20 atx=0 orx= Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis3 / 30 CalculusDifferential CalculusProblem 1: Find the maximum and minimum values off(x) =x3 3x2+20on[ 1,3].Solution:Check endpoints and critical points (f (x) =0).f (x) =3x2 6x,f (x) =0= x=0, (x) =6x 6,f (0)<0 concave down; local max,f (2)>0 concave up; local values:f( 1) =16,f(0) =20,f(2) =16,f(3) = :f(x) =16 atx= 1 orx= :f(x) =20 atx=0 orx= Dylan Johnson (St.)

7 Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis3 / 30 CalculusDifferential CalculusProblem 1: Find the maximum and minimum values off(x) =x3 3x2+20on[ 1,3].Solution:Check endpoints and critical points (f (x) =0).f (x) =3x2 6x,f (x) =0= x=0, (x) =6x 6,f (0)<0 concave down; local max,f (2)>0 concave up; local values:f( 1) =16,f(0) =20,f(2) =16,f(3) = :f(x) =16 atx= 1 orx= :f(x) =20 atx=0 orx= Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis3 / 30 CalculusDifferential CalculusProblem 1: Find the maximum and minimum values off(x) =x3 3x2+20on[ 1,3].

8 Solution:Check endpoints and critical points (f (x) =0).f (x) =3x2 6x,f (x) =0= x=0, (x) =6x 6,f (0)<0 concave down; local max,f (2)>0 concave up; local values:f( 1) =16,f(0) =20,f(2) =16,f(3) = :f(x) =16 atx= 1 orx= :f(x) =20 atx=0 orx= Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis3 / 30 CalculusDifferential CalculusProblem 1: Find the maximum and minimum values off(x) =x3 3x2+20on[ 1,3].Solution:Check endpoints and critical points (f (x) =0).f (x) =3x2 6x,f (x) =0= x=0, (x) =6x 6,f (0)<0 concave down; local max,f (2)>0 concave up; local values:f( 1) =16,f(0) =20,f(2) =16,f(3) = :f(x) =16 atx= 1 orx= :f(x) =20 atx=0 orx= Dylan Johnson (St.)

9 Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis3 / 30 CalculusDifferential CalculusProblem 1: Find the maximum and minimum values off(x) =x3 3x2+20on[ 1,3].Solution:Check endpoints and critical points (f (x) =0).f (x) =3x2 6x,f (x) =0= x=0, (x) =6x 6,f (0)<0 concave down; local max,f (2)>0 concave up; local values:f( 1) =16,f(0) =20,f(2) =16,f(3) = :f(x) =16 atx= 1 orx= :f(x) =20 atx=0 orx= Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis3 / 30 CalculusDifferential CalculusProblem 1: Find the maximum and minimum values off(x) =x3 3x2+20on[ 1,3].

10 Solution:Check endpoints and critical points (f (x) =0).f (x) =3x2 6x,f (x) =0= x=0, (x) =6x 6,f (0)<0 concave down; local max,f (2)>0 concave up; local values:f( 1) =16,f(0) =20,f(2) =16,f(3) = :f(x) =16 atx= 1 orx= :f(x) =20 atx=0 orx= Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis3 / 30 CalculusDifferential CalculusProblem 2: Finddydxify= :Apply logarithm and then useimplicit lny= +x1x(product rule).dydx=y(lnx+1).dydx=xx(lnx+1).Brody Dylan Johnson (St. Louis University) Fundamentals of Engineering Calculus, Differential equations & Transforms, and Numerical Analysis4 / 30 CalculusDifferential CalculusProblem 2: Finddydxify= :Apply logarithm and then useimplicit lny= +x1x(product rule).

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