Calculus A is the first course in the calculus sequence at the University of Notre Dame.
It covers fundamental concepts of differential and integral calculus, focusing on understanding
limits, derivatives, and the basics of integration.
Key Topics Include:
- Functions and Precalculus Foundations: Algebra and function review, exponential and logarithmic functions, and core equation-solving skills used throughout the course.
- Limits and Continuity: Limits from graphs, tables, and algebraic manipulation; continuity; and interpreting/handling discontinuities (including piecewise functions).
- Differentiation: The derivative as a rate of change and slope; differentiation rules (power, product, quotient, chain); derivatives of exponential, logarithmic, and trigonometric functions; and implicit differentiation.
- Applications of Derivatives: Related rates, linearization and percent error, optimization (including closed/bounded intervals), and core theorems (Mean Value Theorem, L’Hôpital’s Rule, first/second derivative tests, and curve sketching).
- Introductory Integration: Antiderivatives, Riemann sums, the Fundamental Theorem of Calculus, and u-substitution.
Exit Tickets:
Exit Tickets
For those attending my Calculus 1/A Tutorial in Spring '26, here is a link to a google drive with all of the tutorial worksheet and quiz keys. Please feel free to use the notes below as additional resources even though they do not line up with the lectures perfectly. view keys
Week01A. Syllabus and Algebra Review
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Week01B. Completing the Square
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Week02A. Quadratic Functions and Exponential Equations
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Week02B. Exponential and Logarithmic Equations
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Week02C. Exponential and Logarithmic Equations Applications
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Week03A. Limits using Charts
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Week03B. Limits using Graphs
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Week03C. Discontinuities and Piecewise functions
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Week04A. Introducing Derivative
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Week04B. Power Rule and Derivatives of Exponential Functions
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Week04C. Derivatives Graphically
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Week05A. Product and Quotient Rule
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Week05. Midterm 01 Review
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Week05b. Derivative of Trig Functions
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Week06B. Chain Rule with Logs
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Week06C. Implicit Differentation
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Week07AII. Related Rates Extra Questions
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Week07B. Parameterization
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Week08A. Linerization Percent Error
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Week08. Midterm 02 Review
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Week08B. Minimums and Maximums
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Week09. FALL BREAK
Week10A. Mean Value Theorem
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Week10B. First Derivative Test
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Week10C. Second Derivative Test
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Week11A. Asymptotes and L'Hopital's Rule
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Week11B. Curve Sketching I
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Week11C. Curve Sketching II
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Week12A. Optimization on a (Closed and) Bounded Region I
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Week12B.Optimization on a (Closed and) Bounded Region II
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Week12C.Optimization on a (Closed and) Bounded Region III
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Week13. Midterm 03 Review
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Week13B. Newton's Method
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Week13C. Antiderivatives
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Week14A. Trig. Antiderivatives
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Week15B. Fundamental Theorem of Calculus
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Week15C. u-Substitution
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Week16A. Second Fundamental Theorem of Calculus
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Week16B. In-class Commentary
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