Notes on basic Calculus concepts.
- Khan academy: AP Calculus BC
- Kristan King: Calculus I (Differential Calculus)
- Kristan King: Calculus II (Integral Calculus)
- Kristan King: Calculus III (Multivariable Calculus)
- The Organic Chemistry Tutor: New Calculus Playlist
- Mathispower4u: Calculus playlist
- Math@Xaktly
- Geoff(x): Teach math using Desmos
- MIT OCW 18.01SC: Single Variable Calculus
- MIT OCW 18.02SC: Multivariable Calculus
- Coursera: Mathematics for Machine Learning: Multivariate Calculus
- Limits and continuity
- Differentiation: definition and basic derivative rules
- Differentiation: composite, implicit, and inverse functions
- Contextual applications of differentiation
- Applying derivatives to analyze functions
- Integration and accumulation of change
- Differential equations
- Applications of integration
- Infinite sequences and series
- ▶ Limit & Continuity
- ▶ Differential Calculus
- Differentiability
- Local linearity & Linear approximation
Basic Differential Rules
- Chain Rule
- Derivatives of Trig functions
- Implicit differentiation
- Higher Order Derivatives
- Derivative of Inverse functions
- Derivative of exponential functions
- Existence Theorems
- L'Hopital's Rule
- Critical points
- Second Derivative Test
- Anti-derivative
- Analyze Function Behaviors with Derivatives
- Optimization
- Applications of Derivatives
- ▶ Integral Calculus
- Definite Integrals
- Antiderivatives
- Fundamental Theorem of Calculus (FTC)
Basic Integral Rules
- Calculate Integrals
- Integration using Trig identities
- Improper Integral
- U-substitution → Chain Rule
- Integrate by Parts → Product Rule
- Partial fractions → Log Rule
- Trig-substitutions → Trig Rule
- Average Value of Functions
- ▶ Differential Equations
- ▶ Applications of definite integrals
- ▶ Series (Calculus)
- Multivariable functions