Why do I need to learn about calculus?
Calculus is a fundamental tool for understanding modern theories and techniques to create software such as artificial intelligence, machine learning, deep learning, data mining, security, digital imagine processing and natural language processing.
What can I do after finishing learning about calculus?
You will then be prepared to be able to learn modern theories and techniques to create security, data mining, image processing or natural language processing software.
What should I do now?
Please read
– this George F. Simmons (1996). Calculus With Analytic Geometry. McGraw-Hill book or
– this C. Henry Edwards David E. Penney (2008). Calculus – Early Transcendentals. Pearson book or
– this George B. Thomas et al. (2018). Thomas’ Calculus: Early Transcendentals. Pearson Education book or
– this James Stewart et al. (2020). Calculus: Early Transcendentals. Cengage Learning book.
Alternatively, please watch
– this MIT 18.01 Single Variable Calculus, Fall 2007 course (Lecture Notes), then watch
– this MIT 18.02 Multivariable Calculus, Fall 2007 course (Lecture Notes). You will need some Linear Algebra knowledge (specifically Inverse Matrix and Determinant) to understand Multivariable Calculus.
When you watch these courses please be sure to refer to
– this George F. Simmons (1996). Calculus With Analytic Geometry. McGraw-Hill book or
– this C. Henry Edwards David E. Penney (2008). Calculus – Early Transcendentals. Pearson book when you have any difficulties with understanding the lectures.
After that please watch this Highlights of Calculus course to review many core concepts of Calculus.
What is the difference between calculus and analysis?
Calculus means a method of calculation. Calculus is about differentiation and integration.
Real analysis includes calculus, and other topics that may not be of interest to engineers but of interest to pure mathematicians such as measure theory, lebesgue integral, topology, functional analysis, complex analysis, PDE, ODE, proofs of theorems.
What does early transcendentals mean?
Transcendentals in this context refers to functions like the exponential, logarithmic, and trigonometric functions.
The early transcendentals approach means that the book introduces polynomial, rational functions, exponential, logarithmic, and trigonometric functions at the beginning, then use them as examples when developing differential calculus. This approach is good for students who do not need to take much rigorous math.
The classical approach is the late transcendentals. It means that the book develops differential calculus using only polynomials and rational functions as examples, then introduces the other functions afterwards. This approach is good for students who need to understand more rigorous definitions of the transcendental functions.
Terminology Review:
- Fundamental Theorem of Calculus.
- L’Hôpital’s Rule.
- Improper Integrals.
- Infinite Series.
- Taylor’s Series.
- Dot Product.
- Cross Product.
- Inverse Matrix.
- Determinant.
- Equations of Planes: ax + by + cz = d
- Parametric Equations = as trajectory of a moving point.
- Velocity Vector
- Acceleration Vector
- Functions of Several Variables
- Partial Derivatives
- Second Derivatives
- Second Derivative Test
- Differentials
After finishing the books please click Topic 17 – Linear Algebra to continue.