Math 118 - Fundamental Principles of the Calculus

Fall 2022

Textbook: Hughes-Hallett, et al., Applied Calculus, 7th Edition.

Office hours: KAP 406B or Zoom. Monday and Friday 9:30AM - 11:00AM.

Email: zzhang51@usc.edu

Lecture notes are based on the textbook.

Lecture 1 - August 22: Review of Linear Functions. (Textbook 1.1 and 1.2)

Lecture notes

Lecture 2 - August 24: Review of Average Rate of Change and Application of Functions on Economics. (Textbook 1.3 and 1.4)

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Lecture 3 - August 26: Review of Exponential Functions and Exponential Growth and Decay. (Textbook 1.5 and 1.7)

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Lecture 4 - August 29: Review of Logarithm and Composition of Functions. (Textbook 1.6 and 1.8)

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Lecture 5 - August 31: Review of Proportionally and Power Functions and Instantaneous Rate of Change. (Textbook 1.9 and 2.1)

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Lecture 6 - September 2: The Derivative Function. (Textbook 2.2)

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Lecture 7 - September 7: Interpretations of The Derivative. (Textbook 2.3)

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Worksheets
Handwritten Lecture Notes

Lecture 8 - September 9: The Second Derivative. (Textbook 2.4)

Lecture notes
Worksheets
Handwritten Lecture Notes

Lecture 9 - September 12: Marginal Cost and Revenue. (Textbook 2.5)

Lecture notes
Worksheets
Handwritten Lecture Notes

Lecture 10 - September 14: Derivative Formulas for Power and Polynomials. (Textbook 3.1)

Lecture 11 - September 16: Derivative of Exponential and Logarithmic Function. (Textbook 3.2)

Lecture 12 - September 19: The Chain Rule. (Textbook 3.3)

Lecture 13 - September 21: Product and Quotient Rules(Textbook 3.4)

Lecture 14 - September 23: Local Maxima and Minima (Textbook 4.1)

Lecture 15 - September 26: Global Maxima and Minima (Textbook 4.3)

Lecture 16 - September 30: Inflection Point (Textbook 4.2)

Lecture 17 - October 3: Profit, Cost, Revenue (Textbook 4.4)

Lecture 18 - October 5: Average Cost (Textbook 4.5)

Lecture 19 - October 7: Elasticity of Demand (Textbook 4.6)

Lecture 20 - October 10: Distance and Accumulated Change and The Definite Integral (Textbook 5.1 and 5.2)

Lecture 21 - October 12: Definite Integral as Area (Textbook 5.3)

Lecture 22 - October 17: Interpretations of The Definite Integral (Textbook 5.4)

Lecture 23 - October 19: Total Change and Fundamental Theorem of Calculus (Textbook 5.5)

Lecture 24 - October 21: Average Value (Textbook 5.6)

Lecture 25 - October 24: Analyzing Antiderivatives Graphically and Numerically (Textbook 6.1)

Lecture 26 - October 26: Antiderivative and the Indefinite Integral (Textbook 6.2)

Lecture 27 - October 28: Using the Fundamental Theorem of Calculus to Find Definite Integrals (Textbook 6.3)

Lecture 28 - October 31: Application: Consumer and Producer Surplus (Textbook 6.4)

Lecture 29 - November 4: Integration by Substitution (Textbook 6.6)

Lecture 30 - November 6: Integration Application: Present and Future Value (Textbook 6.5)

Lecture 31 - November 9: Understanding Functions of Two Variables (Textbook 8.1)

Lecture 32 - November 14: Contour Diagrams (Textbook 8.2)

Lecture 33 - November 16: Partial Derivatives (Textbook 8.3)

Lecture 34 - November 18: Computing Partial Derivatives Algebraically (Textbook 8.4)

Lecture 35 & 36 - November 21 & 28: Critical Points and Optimization (Textbook 8.5)

Lecture 37 - November 30: Constrained Optimization (Textbook 8.6)