Sources: - Calculus - Early Transcendentals (Sullivan, Miranda) - [[Calculus-Early-Transcendentals_Thomas-Weir-Hass.pdf]] - https://www.math.ucdavis.edu/~kouba/ProblemsList.html pre-req: [[Pre-Calculus]] ## Limits and Continuity [[Table of Common limits]] [[Limit (ε, δ)]] [[One-sided Limits]] [[Limit must agree with both one-sided limits]] [[Limit of a Sum or Difference]] [[Limit of a Product]] [[Limit of a Root]] [[Limit of a Rational Exponent]] [[Limit of a Polynomial Function]] [[Limit of a Quotient]] [[Continuity at a Number]] [[Removable Discontinuity]] [[One-Sided Continuity at a Number]] [[Continuity on an Interval]] [[Continuity on a Domain]] [[A polynomial is continuous for all real numbers]] [[A rational function is continuous on its domain]] [[Continuity of a Sum, Difference, Product, and Quotient]] [[Continuity of a Composite Function]] [[Continuity of an Inverse Function]] [[Intermediate Value Theorem]] [[Squeeze Theorem]] [[Limit of sin(𝜃) over 𝜃 at 𝜃=0]] [[Continuity of sin and cos over real numbers]] ## Derivatives [[Table of Derivatives]] [[Slope of the curve]] [[Difference Quotient]] [[Derivative at a point]] [[Derivative of a function]] [[Differentiability implies Continuity]] [[Derivative of a constant function is zero]] [[Power Rule of Derivatives]] [[Derivative Constant Multiple Rule]] [[Derivative of a Sum]] [[Derivative of the natural exponential]] [[Derivative of exponential with other bases]] [[Derivative Product Rule]] [[Derivative Quotient Rule]] [[Higher order derivatives]] [[Derivative of Sine]] [[Derivative of Cosine]] [[Derivative of Tangent]] [[Derivative of Cotangent]] [[Derivative of Secant]] [[Derivative of Cosecant]] [[Derivative Chain Rule]] [[Implicit Differentiation]] [[Normal of a curve]] [[Derivative of an inverse]] [[Derivative of natural logarithm]] [[Derivative of logarithms with other bases]] [[Derivative of arcsine]] [[Derivative of arccosine]] [[Derivative of arctangent]] [[Derivative of arccotangent]] [[Derivative of arcsecant]] [[Derivative of arccosecant]] [[Differential]] ### Applications of derivatives #### Extreme Values and Critical Points [[Extreme Values]] [[Absolute Maximum]] [[Absolute Minimum]] [[Extreme Value Theorem]] [[Relative Maximum]] [[Relative Minimum]] [[Critical Point]] #### Approximation [[Linearization]] [[Differential Approximation]] [[Related Rates Problems]] [[Velocity]] [[Speed]] [[Acceleration]] [[Jerk]] [[g - gravitational acceleration near earths surface]] [[Marginal cost of production]] [[Sensitivity to Change]] #### Theorems [[Rolle's Theorem]] [[Mean Value Theorem]] [[A derivative of zero implies a constant function]] [[Equal derivatives imply a constant difference]] ## Integrals and Anti-Derivatives [[Table of Anti-Derivatives]] ### Applications of Integrals ## Transcendental Functions ## Differential equations ## Series [[Taylor Series for Sine and Cosine]] ## Parametric ## Polar ## Vectors ## Partial Derivatives ## Multiple Integrals ## Integrals and Vector Fields ## Second-Order Differential Equations