Calculus

Calculus#

Table of Contents#

Sections#

Resources#

[P] UT Austin’s calculus

Dawkins, Paul. Paul’s Online Math Notes. Home.

Guichard, David. Calculus: early transcendentals. Home.

YouTube#

blackpenredpen

  • [ y ] 10-18-2023. “finally 0^0 approaches 0 after 6 years!”.

Jacob Koehler https://www.youtube.com/@JacobKoehler

  • [ y ] 04-18-2021. “29 Calculus: Contour Plots in 3D”.

  • [ y ] 04-18-2021. “28 Calculus: Plotting a 3D Function with Python and Matplotlib”.

  • [ y ] 03-27-2021. “18 Calculus: Relating a Function and its Derivative”.

MITOpenCourseWare

  • [ y ] 01-04-2011. “Integral of exp(-x^2) | MIT 18.02SC Multivariable Calculus, Fall 2010”.

Mr P Solver

  • [ y ] 01-17-2022. “SymPy Tutorial (2022): For Physicists, Engineers, and Mathematicians”.

  • [ y ] 08-30-2021. “Integration in PYTHON (Symbolic and Numeric)”.

  • [ y ] 08-09-2021. “Derivatives in PYTHON (Symbolic and Numeric)”.

  • [ y ] 06-28-2021. “Matplotlib Tutorial (2022): For Physicists, Engineers, and Mathematicians”.

  • [ y ] 06-14-2021. “2nd Year Calculus, But in PYTHON”.

  • [ y ] 05-26-2021. “1st Year Calculus, But in PYTHON”.

Prof Ghrist Math https://www.youtube.com/@prof-g

  • [ y ] 06-23-2016 Penn Online Learning. “Calculus Chapter 1 Lecture 1 Functions”.

Steve Brunton

  • [ y ] 01-13-2023. “Solving PDEs with the Laplace Transform: The Wave Equation”.

  • [ y ] 01-09-2023. “Solving PDEs with the Laplace Transform: The Heat Equation”.

  • [ y ] 09-17-2022. “The Wave Equation and Slack Line Physics”.

  • [ y ] 09-17-2022. “The Method of Characteristics and the Wave Equation”.

  • [ y ] 09-17-2022. “Solving the Wave Equation with Separation of Variables… and Guitar String Physics”.

  • [ y ] 09-16-2022. “Deriving the Wave Equation”.

  • [ y ] 09-02-2022. “PDE 101: Separation of Variables! …or how I learned to stop worrying and solve Laplace’s equation”.

  • [ y ] 07-29-2022. “Deriving the Heat Equation in 2D & 3D (& in N Dimensions!) with Control Volumes and Vector Calculus”.

  • [ y ] 07-22-2022. “The Heat Equation and the Steady State Heat Distribution via Laplace’s Equation”.

  • [ y ] 07-15-2022. “Deriving the Heat Equation: A Parabolic Partial Differential Equation for Heat Energy Conservation”.

  • [ y ] 07-08-2022. “Laplace’s Equation and Poisson’s Equation”.

  • [ y ] 07-01-2022. “Partial Differential Equations Overview”.

  • [ y ] 06-17-2022. “Potential Flow Part 2: Details and Examples”.

  • [ y ] 06-10-2022. “Laplace’s Equation and Potential Flow”.

  • [ y ] 05-27-2022. “Are all vector fields the gradient of a potential? … and the Helmholtz Decomposition”.

  • [ y ] 05-20-2022. “Stokes’ Theorem and Green’s Theorem”.

  • [ y ] 05-13-2022. “The Continuity Equation: A PDE for Mass Conservation, from Gauss’s Divergence Theorem”.

  • [ y ] 05-06-2022. “Gauss’s Divergence Theorem”.

  • [ y ] 04-21-2022. “The Curl of a Vector Field: Measuring Rotation”.

  • [ y ] 04-15-2022. “The Divergence of a Vector Field: Sources and Sinks”.

  • [ y ] 04-08-2022. “The Gradient Operator in Vector Calculus: Directions of Fastest Change & the Directional Derivative”.

  • [ y ] 04-01-2022. “Div, Grad, and Curl: Vector Calculus Building Blocks for PDEs [Divergence, Gradient, and Curl]”.

  • [ y ] 03-25-2022. “Vector Calculus and Partial Differential Equations: Big Picture Overview”.

More

  • [ y ] 08-13-2019. Academic Lesson. “Calculus for Beginners full course | Calculus for Machine Learning”.

  • [ y ] 11-03-2020. Aleph 0. “The derivative isn’t what you think it is.”.

  • [ y ] 01-13-2024. The Math Sorcerer. “Why This Old Book Might Just Be Your Best Bet for Learning Calculus”.

  • [ y ] 03-14-2020. Mathologer. “Why did they prove this amazing theorem in 200 different ways? Quadratic Reciprocity MASTERCLASS”.

  • [ y ] 09-02-2021. Tom Rocks Maths. “Oxford Calculus: Jacobians Explained”.

  • [ y ] 02-10-2020. Zach Star. “Dear all calculus students, This is why you’re learning about optimization”.

Terms#

  • [w] Affine Function

  • [w] Affine Space

  • [w] Affine Transformation

  • [w] Algebraic Equation

  • [w] Ambient Space

  • [w] Antiderivative

  • [w] Binomial

  • [w] Boundary Value Problem

  • [w] Bounded Function

  • [w] Calculus

  • [w] Calculus, history

  • [w] Cartesian Coordinates

  • [w] Chain Rule

  • [w] Change of Variables

  • [w] Chord

  • [w] Clairaut’s Theorem

  • [w] Closed-Form Expression

  • [w] Coefficient

  • [w] Compactness

  • [w] Completing the Square

  • [w] Concave Function

  • [w] Conic Section

  • [w] Constant Term

  • [w] Constrained Optimization

  • [w] Constraint

  • [w] Continuous Function

  • [w] Convergent Series

  • [w] Convex Function

  • [w] Critical Point

  • [w] Cubic Function

  • [w] Curl

  • [w] Curvature

  • [w] Curve

  • [w] Cusp (Spinode)

  • [w] Degeneracy

  • [w] Del

  • [w] Derivative

  • [w] Derivative Test

  • [w] Determinant

  • [w] Difference Quotient

  • [w] Differentiable Curve

  • [w] Differentiable Function

  • [w] Differential Calculus

  • [w] Differential Equation

  • [w] Differential Operator

  • [w] Differentiation, linearity

  • [w] Differentiation, notation

  • [w] Differentiation, rules

  • [w] Directional Derivative

  • [w] Divergence

  • [w] Dot Product

  • [w] Eigenvalue

  • [w] Eigenvector

  • [w] Elementary Algebra

  • [w] Equality

  • [w] Equation

  • [w] Euclidean Plane

  • [w] Euclidean Plane Isometry

  • [w] Euclidean Space

  • [w] Expression

  • [w] Extrema

  • [w] Extreme Value Theorem

  • [w] Factorization

  • [w] Feasible Region

  • [w] Fermat’s Theorem

  • [w] Finite Difference

  • [w] Fixed Point

  • [w] Fluxion

  • [w] Fubini’s Theorem

  • [w] Function

  • [w] Fundamental Theorem of Algebra

  • [w] Fundamental Theorem of Calculus

  • [w] Gauss’ Law

  • [w] Gaussian Elimination

  • [w] Gaussian Integral

  • [w] Geometric Transformation

  • [w] Glide Reflection

  • [w] Gradient

  • [w] Graph

  • [w] Green’s Theorem

  • [w] Heine-Borel Theorem

  • [w] Hessian

  • [w] Homothety

  • [w] Hyperplane

  • [w] Hypersurface

  • [w] Implicit Function

  • [w] Implicit Function Theorem

  • [w] Inequality

  • [w] Infinitesimal

  • [w] Inflection Point

  • [w] Integral

  • [w] Integral Operator

  • [w] Intermediate Value Theorem

  • [w] Interval

  • [w] Inverse Function

  • [w] Inverse Function Rule

  • [w] Inverse Function Theorem

  • [w] Irreducible Polynomial

  • [w] Isometry

  • [w] Iterated Integral

  • [w] Jacobian

  • [w] L’Hôpital’s Rule

  • [w] Laplace Operator

  • [w] Laplace Transform

  • [w] Lebesgue Integration

  • [w] Level Curve (Contour Line, Isoline)

  • [w] Level Hypersurface

  • [w] Level Set

  • [w] Level Surface (Isosurface)

  • [w] Limit

  • [w] Limit of a function

  • [w] Line Integral

  • [w] Linear Approximation

  • [w] Linear Map/Transformation

  • [w] Linear Constraint

  • [w] Linear Program (LP)

  • [w] Loss Function

  • [w] Map

  • [w] Map Projections

  • [w] Mathematical Model

  • [w] Matrix

  • [w] Maxima

  • [w] Mean Value Theorem (Lagrange Theorem)

  • [w] Measurable Function

  • [w] Minima

  • [w] Monic Polynomial

  • [w] Monotonic Function

  • [w] Multiple Integral

  • [w] Multivariable Calculus

  • [w] Multivariate Function (Function of Several Variables)

  • [w] Nabla

  • [w] notation for differentiation

  • [w] Numerical Integration

  • [w] Objective Function

  • [w] One-Sided Limit

  • [w] Operator

  • [w] Order of Integration

  • [w] Parametric Equation

  • [w] Partial Derivative

  • [w] Plane

  • [w] Polynomial

  • [w] Power Rule

  • [w] Product Rule

  • [w] Quadratic Equation

  • [w] Quadratic Form

  • [w] Quadratic Formula

  • [w] Quadratic Polynomial

  • [w] Quadric

  • [W] Quartic Function

  • [w] Quotient Rule

  • [w] Rate

  • [w] Reflection

  • [w] Root (Zero)

  • [w] Rotation

  • [w] Rotations and reflections in two dimensions

  • [w] Reciprocal Rule

  • [w] Rolle’s Theorem

  • [w] Saddle Point

  • [w] Scalar Field

  • [w] Scaling

  • [w] Secant

  • [w] Second-Order Derivative

  • [w] Semi Differentiability

  • [w] Sequence

  • [w] Series

  • [w] Shearing

  • [w] Similarity

  • [w] Singular Point

  • [w] Spinode (Cusp)

  • [w] Square

  • [w] Square Number

  • [w] Square Matrix

  • [w] Squeeze Theorem

  • [w] Slope

  • [w] Smoothness

  • [w] Stationary Point

  • [w] Stokes’ Theorem

  • [w] Summation

  • [w] Surface

  • [w] Surface Integral

  • [w] Symbolic Integration

  • [w] Symmetric Matrix

  • [w] Symmetry Operation

  • [w] Tangent

  • [w] Taylor’s Theorem

  • [w] Taylor Series

  • [w] Time Derivative

  • [w] Translation

  • [w] Undefined

  • [w] Unit Ball

  • [w] Unit Cube

  • [w] Unit Disk

  • [w] Unit Hyperbola

  • [w] Unit Sphere

  • [w] Unit Square

  • [w] Vector

  • [w] Vector Calculus

  • [w] Vector Field

  • [w] Vector-Valued Function

  • [w] Vertex

  • [w] Vertical Tangent

Contents