Pre Calculus, Calculus and Trigonometry

Welcome to this course. In this course you will learn Pre Calculus, Calculus and Trigonometry.

Pre Calculus, Calculus and Trigonometry are all important topics of math. “Calculus” is the mathematics of change and because everything in the world is changing, calculus helps us track those changes. It is used in many major fields of modern era like Computer Science, Game Designing, Animation, Mathematical Researches, Statistics & Probability, etc. “Trigonometry” deals with the measurement of sides and angles of triangles and is used many fields including Video Game Designing, Constructions, Flight Engineering, Satellite Navigation System, Oceanography, Astronomy, etc. Knowledge of “Pre Calculus” helps us to understand Calculus better and is good to learn before learning Calculus. 

You will learn the following concepts in this course: 

• Understand FUNCTIONS, learn to Recognize Functions (including the vertical line test) and cite examples thereof; (Pre Calculus)

• Understand the Domain and Range of a function and learn to find them for a given function; (Pre Calculus)

• Understand the Average Rate of Change of a function, learn to find the Average Rate of Change of a function and solve problems based on them; (Pre Calculus)

• Learn about Even and Odd Functions and cite examples thereof; (Pre Calculus)

• Learn to determine if a given function is Even, Odd, or neither; (Pre Calculus)

• Learn about Composition of Functions (composite functions), learn to find the Composition of Two Functions and solve problems based on them; (Pre Calculus)

• Learn about the Inverse Function, learn to find the Inverse of any given Function; (Pre Calculus)

• Understand the Absolute and Relative Maxima and Minima of a Function, learn to Find the Absolute and Relative Maxima and Minima of a given function from graphs; (Pre Calculus)

• Understand TRIGONOMETRY, understand Triangles, the Types of Triangles, and cite examples thereof; (Trigonometry)

• Learn the Properties of Triangles and solve problems based on them; (Trigonometry)

• Understand Pythagoras Theorem, and use it to solve right triangles; (Trigonometry)

• Learn Trigonometric Functions sin, cos, tan and find them for any given right triangle; (Trigonometry)

• Learn Trigonometric Functions cosec, sec, cot and find them for any given right triangle; (Trigonometry)

• Learn about the Trigonometric Functions of Standard Angles of Trigonometry (namely 0 degree, 30 degree, 45 degree, 60 degree and 90 degree); (Trigonometry)

• Understand Complementary angles, Learn to find Find the Complementary Angle of any given angle; (Trigonometry)

• Master all the Trigonometric Identities namely,Complementary Angle Identities, Pythagorean Identities, Sum and Difference of Angles Formulas, Negative Angle Identities, Sum to Product Formulas, Product to Sum Formulas, and apply these Trigonometric Identities in solving problems; (Trigonometry)

• Learn to Find the Trigonometric Function values of Non-Standard Angles (like that of 75 degree, 22.5 degree, etc.) using Trigonometric Identities; (Trigonometry)

• Understand Laws of Sines and Cosines and use them to Find the Unknown Sides and Angles of a given Triangle;

• Learn about Similar Triangles; (Trigonometry)

• Understand the Conditions for Similarity of Two Triangles; (Trigonometry)

• Learn to Prove the Similarity of Given Triangles; (Trigonometry)

• Learn the Properties of Similar Triangles and solve problems to Find Unknown Sides and Angles of Similar Triangles; (Trigonometry)

• Understand the concept of LIMIT of a Function, learn to Find the Limit of a function using graphs; (Calculus)

• Understand One-Sided Limits (left hand and right hand limits, learn to Find One-Sided Limits from graphs and solve problems based on them; (Calculus)

• Understand the CONTINUITY of a function, learn to Find the Continuity of a given function from graphs and solve problems based on them; (Calculus)

• Detailed understand of DERIVATIVES; (Calculus)

• Learn about the Standard Derivative Formula (the first principle) and use it for finding the derivatives; (Calculus)

• Learn the Different Derivative rules such as Derivative of a Constant, Multiplication by Constant, Power Rule, Sum Rule, Difference Rule, Product Rule, Quotient Rule, Reciprocal Rule and the important Chain rule; (Calculus)

• Learn to Find the Derivatives of functions using the Different Derivative Rules (with lots of examples on the same); (Calculus)

• Learn to Find Derivatives of Trigonometric Functions (a.k.a Trigonometric Derivatives) (with lots of practice examples); (Calculus)

• Learn to Find Derivatives of Exponential Functions (a.k.a Exponential Derivatives) (with lots of practice examples); (Calculus)

• Learn to Find Derivatives of Logarithmic Functions (a.k.a. Logarithmic Derivatives) (with lots of practice examples); (Calculus)

Overall, after completing this course, you will have a very clear understanding of the topics of Pre Calculus, Calculus and Trigonometry covered in this course, with sound ability to solve problems.

Who this course is for:

• Math Majors.
• Engineering Majors.
• Working Professionals.
• Anybody interested in learning Functions (Pre Calculus), Trigonometry and Calculus 1.