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Calculus I - MATH 151

Covers limits, continuity, derivatives, applications of derivatives, integrals, and the Fundamental Theorem of Calculus.

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Study guides

6

4 Applications of Derivatives

A clear progression through the main applications of derivatives: modeling changing quantities, approximating values, analyzing extrema and graph shape, applying the Mean Value Theorem, and solving optimization problems.
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5 Integrals and Their Applications

A progressive guide to antiderivatives, definite integrals, Riemann sums, the Fundamental Theorem of Calculus, integral properties, and substitution techniques.
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3 The Derivative and Differentiation Rules

A progressive guide to defining derivatives, interpreting instantaneous change, and applying the main differentiation rules to explicit and implicit functions.
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2 Limits and Continuity

A progressive guide to interpreting, calculating, and applying limits, asymptotes, continuity, and the Intermediate Value Theorem.
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6 The Fundamental Theorem of Calculus

A clear progression through the Fundamental Theorem of Calculus, definite integrals, accumulation, net change, average value, and introductory applications of integration.
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1 Functions, Rates of Change, and the Idea of a Limit

Build a connected understanding of functions, rates of change, secant and tangent lines, and limits as the foundation for differential calculus.
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Quizzes

6

1 Functions, Rates of Change, and the Idea of a Limit

A medium-difficulty quiz on functions, rates of change, secant and tangent lines, and limits. Questions progress from foundational interpretation to applied reasoning and explanation.
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2 Limits and Continuity

A medium-difficulty quiz on limits, one-sided limits, infinite behavior, asymptotes, continuity, algebraic limit evaluation, and the Intermediate Value Property.
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4 Applications of Derivatives

A medium-difficulty quiz on applying derivatives to related rates, approximation, extrema, the Mean Value Theorem, monotonicity, concavity, motion, Newton's method, marginal analysis, and curve analysis.
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3 The Derivative and Differentiation Rules

A medium-difficulty quiz on derivative definitions, interpretations, differentiation rules, common derivatives, the chain rule, and implicit differentiation.
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5 Integrals and Their Applications

A medium-difficulty quiz on antiderivatives, definite integrals, Riemann sums, the Fundamental Theorem of Calculus, integral properties, and substitution. The questions emphasize interpreting and applying the ideas rather than recalling isolated definitions.
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6 The Fundamental Theorem of Calculus

A medium-difficulty quiz on the Fundamental Theorem of Calculus, definite integrals, accumulation, net change, average value, and applications of integration. Questions progress from conceptual understanding to multistep calculation and explanation.
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Flashcards

6

2 Limits and Continuity

A focused review of limits, one-sided and infinite behavior, asymptotes, continuity, discontinuities, and the Intermediate Value Property.
Flashcards · Updated

5 Integrals and Their Applications

Builds core fluency with antiderivatives, definite integrals, Riemann sums, the Fundamental Theorem of Calculus, integral properties, and substitution.
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4 Applications of Derivatives

Review how derivatives model rates, approximate values, classify extrema, analyze graph behavior, and solve optimization and motion problems.
Flashcards · Updated

1 Functions, Rates of Change, and the Idea of a Limit

A focused introduction to functions, domains, rates of change, secant and tangent lines, and limits as the foundation of derivatives.
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6 The Fundamental Theorem of Calculus

A focused review of antiderivatives, both parts of the Fundamental Theorem of Calculus, signed accumulation, and core integration applications.
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3 The Derivative and Differentiation Rules

A focused review of derivative definitions, interpretations, differentiation rules, common derivatives, the chain rule, and implicit differentiation.
Flashcards · Updated