Current courses

N/A

Previous courses

• Fall 2025 - University of Utah MATH 1220: Syllabus
• Summer 2025 - ↷Mathematics Program for High School Students
• Spring 2025 - University of Utah MATH 1220: Syllabus
• Fall 2024 - University of Utah MATH 1210: Syllabus
• Summer 2024 - ↷pre-REU: Expanding circle maps, digit expansions and topological Markov chains
• Spring 2024 - University of Utah MATH 2210: Syllabus
• Summer 2023 - University of Utah MATH 3210: Syllabus
• Spring 2023 - University of Utah MATH 1320
• Fall 2022 - University of Utah MATH 1320

Notes

Upon request, I’ve compiled my handwritten notes for various courses below. They all likely have mistakes, and I’m happy to fix them if you let me know. Some of the notes have section numbers; this was following a specific textbook at the time, but the notes are largely independent.

Calculus

• Limits
• Limits, formally
• Computing limits
• Trig limits
• Asymptotes
• Continuity and IVT
• Rate of change
• Derivatives
• Sums, powers, products, and quotients
• Trig derivatives
• Chain rule
• Higher-order derivatives
• Implicit differentiation and inverse functions
• Related rates
• Linear approximation and error
• Extreme value theorem and critical points
• Monotonicity and concavity
• Local extrema
• Optimization problem
• Mean value theorem
• Numerical methods for root finding
• Antiderivatives
• Differential equations
• Computing area, approximately
• Computing area, exactly
• FTC part 1
• FTC part 2
• Mean value theorem, revisited
• Areas, revisited
• Solids of Revolution, Washers
• Solids of Revolution, Shells
• Arc length
• Energy in lifting a fluid
• Logarithms, the calculus way
• Inverse function theorem
• The number e
• Calculus with different base exponentials/logs
• Common ODEs
• First-order linear ODE
• Euler’s method
• Inverse trig functions
• Hyperbolic trig functions
• u-Substitution
• Integration by parts
• Trig integrals
• Integrals with radicals
• Integrating rational functions
• Special functions and integration flowchart
• L’Hôpital’s rule (0/0 form)
• Other uses of L’Hôpital’s rule
• Infinite bounds of integration
• Integrating with vertical asymptotes

Additional notes to be posted shortly.

Tutoring

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