Calculus / Honors College Mathematics
The Mathematics of Change

Limits · Derivatives · Integrals · Mastered

The most comprehensive agentic Honors Calculus course available. Master all 8 units, build deep mathematical reasoning, and achieve college math readiness — powered by Prof. Sofia Euler and SofAI. UC A-G Section C approved. Honors credit with +1.0 GPA weighting.

Limits & Continuity

Build rigorous understanding of how functions behave near points. Master limit laws, one-sided limits, continuity definitions, and the foundational theorems that underpin all of calculus.

Differential Calculus

Develop fluency with all differentiation techniques — power, product, quotient, chain rule, implicit differentiation — and apply them to rates of change, optimization, and graph analysis.

Integral Calculus

Master the Fundamental Theorem of Calculus, antiderivatives, definite integrals, Riemann sums, and u-substitution. Connect integration to accumulation and net change.

Applications & Modeling

Apply calculus to real contexts: differential equations, exponential models, area between curves, volumes of solids, particle motion, and mathematical proof-writing.

Master derivative rules until they are automatic — power, product, quotient, chain, and implicit. These appear in every unit from here forward.

Understand both parts of the FTC deeply, not just the formula. Know WHY d/dx ∫ₐˣ f(t)dt = f(x) and what it means geometrically.

Build sign charts for f'(x) and f''(x) on every graph-analysis problem. They reveal increasing/decreasing, concavity, and all extrema systematically.

Write every step — even steps that feel obvious. Mathematical justification is the skill being assessed, not just the final numerical answer.

Separation of variables follows a strict sequence: separate → integrate both sides → include +C → apply initial condition → write particular solution.

Connect calculus to real-world context in every application problem. Ask: what does this derivative mean physically? What does this integral accumulate?

Three Assessment Types

Honors Calculus assessments emphasize rigorous mathematical reasoning, complete justification, and real-world application — the skills that distinguish college-ready mathematicians.

Phase 1: Limits and Differentiation (Units 1–3) — foundations

• Master limit laws, one-sided limits, and continuity definitions
• Learn all derivative rules: power, product, quotient, chain rule
• Implicit differentiation and inverse function derivatives
• Daily practice: 10 derivative problems from PatrickJMT or Krista King

Phase 2: Applications and Integration (Units 4–6) — conceptual depth

• Related rates and particle motion (Units 4–5)
• Critical points, first/second derivative tests, optimization
• Introduction to integration: Riemann sums, FTC Parts 1 & 2
• U-substitution practice — 10 problems per day

Phase 3: Differential Equations, Integration Applications, Proof Writing

• Slope fields, separation of variables, Euler's method (Unit 7)
• Area between curves, disk/washer volume, average value (Unit 8)
• Complete 2 full timed problem sets per week with self-scoring
• Work through past FRQs (2014–2024) as extended practice problems

Phase 4: Application Projects, Proof Mastery, and Course Synthesis

• Complete Application Project with written modeling analysis
• Review every missed concept with Prof. Sofia (SofAI chat)
• Full course formula review: all derivative and integral rules from memory
• Synthesize connections across all 8 units in written reflection