References – Basic Calculus

Basic Calculus – Limits & Continuity

Introduction:

https://byjus.com/maths/limits-and-continuity/

Importance:

https://www.khanacademy.org/math/calculus-1/cs1-limits-and-continuity

Real Life Situation:

https://prezi.com/r9hprj456bjd/limits-and-continuity-in-reality/#:~:text=Real%20life%20Limits,These%20approximations%20always%20use%20limits.

Subtopics Importance:

Limit of a function using a table of  values and the graph of the function

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_2_Limits/2.2%3A_Limits_of_Functions

Limit laws 

https://openstax.org/books/calculus-volume-1/pages/2-3-the-limit-laws

Limits of exponential, logarithmic,  and trigonometric functions using tables of values  and graphs of the functions

http://help.mathlab.us/159-limit-of-an-exponential-and-logarithmic-function.html

Continuity of a function at a number 

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_2_Limits/2.6%3A_Continuity

Continuity of a function on an interval

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_2_Limits/2.6%3A_Continuity

Basic Calculus – Derivatives

Introduction:

https://www.britannica.com/science/derivative-mathematics

Importance:

Why are Derivatives Important?

Real Life Situation:

https://www.investopedia.com/ask/answers/12/derivative.asp

Subtopics Importance:

Rules for Differentiation

https://www.siyavula.com/read/maths/grade-12/differential-calculus/06-differential-calculus-03

Chain Rule

https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-1a/a/chain-rule-review

Derivatives

https://www.britannica.com/science/derivative-mathematics

Differentiation of Algebraic, Exponential, and Trigonometric Functions

Click to access Exp_log_trig.pdf

Higher-Order Derivatives

https://www.cliffsnotes.com/study-guides/calculus/calculus/the-derivative/higher-order-derivatives

Implicit Differentiation

https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-2-new/ab-3-2/a/implicit-differentiation-review

Derivative of a Function to the Slope of the Tangent Line

http://clas.sa.ucsb.edu/staff/lee/Secant,%20Tangent,%20and%20Derivatives.htm#:%7E:text=A%20tangent%20line%20is%20a,same%20point%20(See%20below.)

Basic Calculus – Integration

Introduction:

https://www.britannica.com/science/integral-mathematics

Importance:

https://www.emathzone.com/tutorials/calculus/introduction-to-integral-calculus.html

Real Life Situation:

https://mathhints.com/applications-integration-area-volume/

Subtopics Importance:

Integral

https://www.britannica.com/science/integral-mathematics

https://www.cuemath.com/calculus/applications-of-integrals/

Definite integral of a function using the Fundamental Theorem of Calculus

5.3 The Fundamental Theorem of Calculus

Definite integral of a function using the substitution rule

https://math.libretexts.org/Courses/Mount_Royal_University/MATH_1200%3A_Calculus_for_Scientists_I/4%3A_Integral_Calculus/4.7%3A_Definite_integrals_by_substitution.

Area of a plane region using the definite integrals

6.1 Areas between Curves

https://www.brightstorm.com/math/calculus/the-definite-integral/definite-integrals-and-area/