Videos for the lecture notes of MA 138 are posted below. Each lecture has been broken into several videos for your convenience.
You are encouraged to watch the videos in advance before class.
Course Introduction:
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Course Introduction Course Introduction (4 x page format)
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Lecture 1:
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Review of integration; application of integration (Section 6.3): pp. 334-351 of our textbook
January 8, 2024
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Lecture 2:
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Applications of integration (Section 6.3): pp. 334-351 of our textbook
January 10, 2024
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Lecture 3:
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The substitution rule (Section 7.1): pp. 355-364 of our textbook
January 12, 2024
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Lecture 4:
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Integration by parts and practicing integration (Section 7.2): pp. 365-373 of our textbook
January 17, 2024
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Lecture 5:
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Integration by parts and practicing integration (Section 7.2): pp. 365-373 of our textbook
January 19, 2024
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Lecture 6:
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Rational functions and partial fractions (Section 7.3): pp. 374-387 of our textbook
January 22, 2024
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Lecture 7:
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Rational functions and partial fractions (Section 7.3): pp. 374-387 of our textbook
January 24, 2024
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Lecture 8:
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Improper integrals (Section 7.4): pp. 388-398 of our textbook
January 26, 2024
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Lecture 9:
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Improper integrals (Section 7.4): pp. 388-398 of our textbook
January 29, 2024
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Lecture 10:
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Improper integrals (Section 7.4): pp. 388-398 of our textbook
January 31, 2024
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Lecture 11:
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Solving differential equations (Section 8.1): pp. 428-441 of our textbook
February 2, 2024
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Lecture 13:
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Solving differential equations (Section 8.1): pp. 428-441 of our textbook
February 7, 2024
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Lecture 14:
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Solving differential equations (Section 8.1): pp. 428-441 of our textbook
February 9, 2024
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Lecture 15:
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Direction fields and SAGE: handout
February 12, 2024
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Lecture 15 Lecture 15 with answers (4 x page format)
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YouTube Playlist with videos for Lecture 15
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Sage is a free open-source mathematics software system that is useful to produce, for our purposes,
direction fields of differential equations of the first order. In particular, the SageMathCell project is
an easy-to-use web interface. Just access the website https://sagecell.sagemath.org and type
some Sage codes in the provided box and then press Evaluate.
For example, the Sage codes to produce the direction field of the DE dy/dx= x^2*y^2 are:
x,y=var('x,y')
plot_slope_field(x^2*y^2,(x,-5,5),(y,-10,10), headaxislength=3, headlength=3)
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Lecture 16:
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Direction fields and SAGE: handout
February 14, 2024
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Lecture 17:
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Equilibria and their stability (Section 8.2): pp. 441-454 of our textbook
February 16, 2024
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Lecture 18:
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Equilibria and their stability (Section 8.2): pp. 441-454 of our textbook
February 19, 2024
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Lecture 19:
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Linear systems (Section 9.1): pp. 487-500 of our textbook
February 21, 2024
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Lecture 20:
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Linear systems (Section 9.1): pp. 487-500 of our textbook
February 23, 2024
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Lecture 21:
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Matrices (Section 9.2): pp. 501-518 of our textbook
February 26, 2024
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Lecture 22:
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Matrices (Section 9.2): pp. 501-518 of our textbook
February 28, 2024
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Lecture 23:
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Linear Maps (9.3): pp. 518-535 of our textbook
March 1, 2024
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Lecture 25:
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Eigenvectors and Eigenvalues (9.3): pp. 518-535 of our textbook
March 6, 2024
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Lecture 26:
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Eigenvectors and Eigenvalues (9.3): pp. 518-535 of our textbook
Fibonacci's numbers, a population model, and powers of matrices: handout
March 8, 2024
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Lecture 27:
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Eigenvectors and Eigenvalues (9.3): pp. 518-535 of our textbook
Fibonacci's numbers, a population model, and powers of matrices: handout
March 18, 2024
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Lecture 28:
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Curve Fitting- Least Square Approximation: handout
March 20, 2024
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Lecture 29:
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Curve Fitting- Least Square Approximation: handout
March 22, 2024
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Lecture 30:
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Functions of Two or More Independent Variables (Section 10.1): pp. 563-575 of our textbook
March 25, 2024
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Lecture 31:
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Limits and Continuity (Section 10.2): pp. 575-582 of our textbook
March 27, 2024
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Lecture 32:
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Partial Derivatives (Section 10.3): pp. 582-589 of our textbook
March 29, 2024
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Lecture 33:
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Partial Derivatives (Section 10.3): pp. 582-589 of our textbook
April 1, 2024
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Lecture 34:
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Tangent Planes, Differentiability, and Linearization (Section 10.4): pp. 589-599 of our textbook
April 3, 2024
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Lecture 35:
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Tangent Planes, Differentiability, and Linearization (Section 10.4): pp. 589-599 of our textbook
April 5, 2024
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Lecture 36:
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Vector Valued Functions (Section 10.4): pp. 589-599 of our textbook
April 8, 2024
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Lecture 37:
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Linear Systems - Theory (Section 11.1): pp. 655-676 of our textbook
April 10, 2024
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Lecture 38:
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Linear Systems - Theory (Section 11.1): pp. 655-676 of our textbook
April 12, 2024
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Lecture 39:
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Linear Systems - Theory (Section 11.1): pp. 655-676 of our textbook
April 15, 2024
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Lecture 40:
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Linear Systems - Applications (Section 11.2): pp. 677-687 of our textbook
April 17, 2024
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Lecture 41:
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Nonlinear Autonomous Systems - Theory (Section 11.3): pp. 688-698 of our textbook
April 19, 2024
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Lecture 42:
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Nonlinear Autonomous Systems - Theory (Section 11.3): pp. 688-698 of our textbook
April 22, 2024
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Lecture 43:
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Nonlinear Systems - A model for Epidemics (Section 11.5.5): pp. 718-730 of our textbook
April 24, 2024
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