> For the complete documentation index, see [llms.txt](https://solomons-mathbook.gitbook.io/calculus-basics/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://solomons-mathbook.gitbook.io/calculus-basics/master.md). # Introduction ## Study resources * [x] [Khan academy: AP Calculus BC](https://www.khanacademy.org/math/ap-calculus-bc) * [x] [Kristan King: Calculus I (Differential Calculus)](https://www.youtube.com/playlist?list=PLJ8OrXpbC-BOYyyC-Gunxrh-jYnSfsQy0) * [x] [Kristan King: Calculus II (Integral Calculus)](https://www.youtube.com/playlist?list=PLJ8OrXpbC-BMdeuQfJDVRJ5DPMduSzVow) * [x] [Kristan King: Calculus III (Multivariable Calculus)](https://www.youtube.com/playlist?list=PLJ8OrXpbC-BMObozItpbiZ8f2pjf3qS9M) * [x] [The Organic Chemistry Tutor: New Calculus Playlist](https://www.youtube.com/playlist?list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv) * [x] [Mathispower4u: Calculus playlist](http://www.mathispower4u.com/calculus.php) * [x] [Math@Xaktly](http://xaktly.com/XMathMain.html) * [x] [Geoff(x): Teach math using Desmos](https://www.geoffofx.com/) * [ ] [MIT OCW 18.01SC: Single Variable Calculus](https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/index.htm) * [ ] [MIT OCW 18.02SC: Multivariable Calculus](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/) * [ ] [Coursera: Mathematics for Machine Learning: Multivariate Calculus](https://www.coursera.org/learn/multivariate-calculus-machine-learning/home/welcome) ## Study Tools * [x] [Symbolab](https://www.symbolab.com/) * [x] [Desmos](https://www.desmos.com/calculator) * [x] [GeoGebra](https://www.geogebra.org/3d?lang=en) * [ ] [MIT Mathlets](http://mathlets.org/mathlets/) * [ ] [TAYLOR POLYNOMIALS](http://mathlets.org/mathlets/taylor-polynomials/) * [ ] [HARMONIC FREQUENCY RESPONSE: VARIABLE INPUT FREQUENCY](http://mathlets.org/mathlets/harmonic-frequency-response-i/) ## Practice To-do List (Linked with Unit tests) * [x] [Limits and continuity](https://www.khanacademy.org/math/ap-calculus-bc/bc-limits-new/modal/test/bc-limits-optional-unit-test) * [x] [Differentiation: definition and basic derivative rules](https://www.khanacademy.org/math/ap-calculus-bc/bc-differentiation-1-new/modal/test/bc-diff-1-optional-unit-test) * [x] [Differentiation: composite, implicit, and inverse functions](https://www.khanacademy.org/math/ap-calculus-bc/bc-differentiation-2-new/modal/test/bc-diff-2-optional-unit-test) * [x] [Contextual applications of differentiation](https://www.khanacademy.org/math/ap-calculus-bc/bc-diff-contextual-applications-new/modal/test/bc-diff-context-optional-unit-test) * [x] [Applying derivatives to analyze functions](https://www.khanacademy.org/math/ap-calculus-bc/bc-diff-analytical-applications-new/modal/test/bc-5-13-unit-test) * [x] [Integration and accumulation of change](https://www.khanacademy.org/math/ap-calculus-bc/bc-integration-new/modal/test/bc-integration-optional-unit-test) * [x] [Differential equations](https://www.khanacademy.org/math/ap-calculus-bc/bc-differential-equations-new/modal/test/bc-7-9-unit-test) * [x] [Applications of integration](https://www.khanacademy.org/math/ap-calculus-bc/bc-applications-of-integration-new/modal/test/bc-8-14-unit-test) * [x] [Infinite sequences and series](https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/modal/test/bc-series-optional-unit-test) ## `Table of Contents` * [▶ Limit & Continuity](/calculus-basics/comment-389065252.md) * [Limit properties & Limits of Combined Functions](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-388416883.md) * [Limits at infinity](/calculus-basics/comment-389065252/comment-389097947.md) * [All types of discontinuities](/calculus-basics/comment-389065252/comment-389112016.md) * [▶ Differential Calculus](/calculus-basics/comment-389389887.md) * [Differentiability](/calculus-basics/comment-389389887/comment-389450771.md) * [Local linearity & Linear approximation](/calculus-basics/comment-389389887/comment-389748831.md) * [`Basic Differential Rules`](/calculus-basics/comment-389389887/comment-390102382.md) * [Chain Rule](/calculus-basics/comment-389389887/comment-390151930.md) * [Derivatives of Trig functions](/calculus-basics/comment-389389887/comment-390171964.md) * [Implicit differentiation](/calculus-basics/comment-389389887/comment-390174936.md) * [Higher Order Derivatives](/calculus-basics/comment-389389887/comment-390403740.md) * [Derivative of Inverse functions](/calculus-basics/comment-389389887/comment-390571646.md) * [Derivative of exponential functions](/calculus-basics/comment-389389887/comment-390593003.md) * [Existence Theorems](/calculus-basics/comment-389389887/comment-390951282.md) * [L'Hopital's Rule](/calculus-basics/comment-389389887/comment-391295798.md) * [Critical points](/calculus-basics/comment-389389887/comment-391300278.md) * [Extrema: Maxima & Minima](/calculus-basics/comment-389389887/comment-391300278/comment-391968249.md) * [Concavity](/calculus-basics/comment-389389887/comment-391300278/comment-391981189.md) * [Inflection Point](/calculus-basics/comment-389389887/comment-391300278/comment-391988411.md) * [Second Derivative Test](/calculus-basics/comment-389389887/comment-392000339.md) * [Anti-derivative](/calculus-basics/comment-389389887/comment-392626418.md) * [Analyze Function Behaviors with Derivatives](/calculus-basics/comment-389389887/comment-392679635.md) * [Optimization](/calculus-basics/comment-389389887/comment-392767038.md) * [Applications of Derivatives](/calculus-basics/comment-389389887/comment-392796710.md) * [Motion problems](/calculus-basics/comment-389389887/comment-392796710/comment-393474147.md) * [Planar motion](/calculus-basics/comment-389389887/comment-392796710/comment-393484574.md) * [▶ Integral Calculus](/calculus-basics/comment-394073989.md) * [Definite Integrals](/calculus-basics/comment-394073989/comment-394263665.md) * [Antiderivatives](/calculus-basics/comment-394073989/comment-394270551.md) * [Fundamental Theorem of Calculus (FTC)](/calculus-basics/comment-394073989/comment-395305706.md) * [`Basic Integral Rules`](/calculus-basics/comment-394073989/comment-395356656.md) * [Calculate Integrals](/calculus-basics/comment-394073989/comment-395370129.md) * [Integration using Trig identities](/calculus-basics/comment-394073989/comment-395370247.md) * [Improper Integral](/calculus-basics/comment-394073989/comment-395404568.md) * [U-substitution → Chain Rule](/calculus-basics/comment-394073989/comment-395677669.md) * [Integrate by Parts → Product Rule](/calculus-basics/comment-394073989/comment-395694311.md) * [Partial fractions → Log Rule](/calculus-basics/comment-394073989/comment-395949004.md) * [Trig-substitutions → Trig Rule](/calculus-basics/comment-394073989/comment-395950727.md) * [Average Value of Functions](/calculus-basics/comment-394073989/comment-395952635.md) * [▶ Differential Equations](/calculus-basics/comment-396484900.md) * [Parametric Equations Differentiation](/calculus-basics/comment-396484900/comment-396505172.md) * [Separable Differential Equations](/calculus-basics/comment-396484900/comment-396517400.md) * [Specific antiderivatives](/calculus-basics/comment-396484900/comment-396520824.md) * [Polar Curve Functions (Differential Calc))](/calculus-basics/comment-396484900/comment-396527546.md) * [Logistic Growth Model](/calculus-basics/comment-396484900/comment-396537354.md) * [Slope Field](/calculus-basics/comment-396484900/comment-396852129.md) * [Euler's Method](/calculus-basics/comment-396484900/comment-396852203.md) * [▶ Applications of definite integrals](https://github.com/solomonxie/solomonxie.github.io/issues/49) * [Area under Rate function](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-398313540.md) * [Motion problems](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-398340530.md) * [Planar motion](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-398346952.md) * [Function Area between curve & axes](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-398360666.md) * [Area of Polar Curves (Integral Calc)](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-398657472.md) * [Arc Length](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-398693215.md) * [Parametric Curve Arc Length](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-398698980.md) * [Volumes of 3D Solids](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-398739105.md) * [Disc Method](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-399024510.md) * [Washer Method](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-399040648.md) * [Shell Method](https://github.com/solomonxie/gitbook-calculus-basics/tree/8aa3e991de2092e837785baf205988be68615205/comment-399051413.md) * [▶ Series (Calculus)](/calculus-basics/comment-399637419.md) * [Infinite Seires](/calculus-basics/comment-399637419/comment-399648088.md) * [Infinite Geometric Series](/calculus-basics/comment-399637419/comment-399649974.md) * [Convergence Tests](/calculus-basics/comment-399637419/comment-399657906.md) * [nth Term Test](/calculus-basics/comment-399637419/comment-399657906/comment-399662214.md) * [Integral Test](/calculus-basics/comment-399637419/comment-399657906/comment-399662247.md) * [p-series Test](/calculus-basics/comment-399637419/comment-399657906/comment-399662321.md) * [Comparison Test](/calculus-basics/comment-399637419/comment-399657906/comment-399673966.md) * [Ratio Test](/calculus-basics/comment-399637419/comment-399657906/comment-399674089.md) * [Root Test](/calculus-basics/comment-399637419/comment-399657906/comment-399949602.md) * [Alternating Series Test](/calculus-basics/comment-399637419/comment-399657906/comment-400220808.md) * [Absolute vs. Conditional Convergence](/calculus-basics/comment-399637419/comment-400234993.md) * [Error Estimation of Alternating Series](/calculus-basics/comment-399637419/comment-400234993/comment-400239322.md) * [Error Estimation Theorem](/calculus-basics/comment-399637419/comment-400234993/comment-400584670.md) * [Interval of Convergence](/calculus-basics/comment-399637419/comment-400234993/comment-401284580.md) * [Power Series](/calculus-basics/comment-399637419/comment-401305392.md) * [Taylor Series](/calculus-basics/comment-399637419/comment-401305392/comment-401713162.md) * [Maclaurin Series](/calculus-basics/comment-399637419/comment-401305392/comment-401714233.md) * [Lagrange Error Bound](/calculus-basics/comment-399637419/comment-401305392/comment-402061178.md) * [Finding Taylor series for a function](/calculus-basics/comment-399637419/comment-401305392/comment-402936936.md) * [Function as a Geometric Series](/calculus-basics/comment-399637419/comment-401305392/comment-402940086.md) * [Maclaurin Series of Common functions](/calculus-basics/comment-399637419/comment-401305392/comment-402940122.md) * [Euler's Formula & Euler's Identity](/calculus-basics/comment-399637419/comment-401305392/comment-402953466.md) * [Multivariable functions](/calculus-basics/comment-408792974.md) * [Parametric Functions](/calculus-basics/comment-408792974/comment-408793195.md) * [Partial derivatives](/calculus-basics/comment-408792974/comment-408796701.md) * [Gradient](/calculus-basics/comment-408792974/comment-408796819.md)