Pre Calculus, Calculus and Trigonometry
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 By the end of this course you will be able to define functions, recognize them and cite examples thereof (pre calculus);
 define the domain and range of a function, find the domain and range of a function (pre calculus);
 define the average rate of change of a function, find the average rate of change of a function and solve problems based on them (pre calculus);
 define even and odd functions and cite examples thereof (pre calculus);
 determine if a given function is even, or odd, or none (pre calculus);
 define function compositions (pre calculus);
 find the composition of two functions and solve problems based on them (pre calculus);
 define the inverse function (pre calculus);
 find the inverse of a function and solve problems based on them (pre calculus);
 define the absolute and relative maxima and minima of a function (pre calculus);
 find the absolute and relative maxima and minima from graphs (pre calculus);
 define the increasing and decreasing intervals of a function (pre calculus);
 find the increasing and decreasing intervals from graphs (pre calculus); and
 define triangles, define the types of triangles, and cite examples thereof (trigonometry);
 define the properties of triangles and solve problems based on them (trigonometry);
 define pythagoras theorem, and use it to solve right triangles (trigonometry);
 define trigonometric functions sin, cos, tan and find them for any given right triangle (trigonometry);
 define trigonometric functions cosec, sec, cot and find them for any given right triangle (trigonometry);
 define the trigonometric functions of standard angles of trigonometry (namely 0 degree, 30 degree, 45 degree, 60 degree and 90 degree) (trigonometry);
 define complementary angles, find the complementary angle of any given angle (trigonometry);
 define 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);
 find the Trigonometric Function values of NonStandard Angles (like that of 75 degree, 22.5 degree, etc.) using Trigonometric Identities (trigonometry);
 define laws of sines and cosines and use them to find the unknown sides and angles of a given triangle (trigonometry);
 define similar triangles (trigonometry);
 define the conditions for similarity of two triangles (trigonometry);
 define the properties of similar triangles and solve problems to find unknown sides and angles of similar triangles (trigonometry);
 prove the similarity of two triangles (trigonometry);
 define limit of a function (Calculus);
 find the limit of a function using graphs and solve problems based on them (Calculus);
 define onesided limits (Calculus);
 find onesided limits from graphs and solve problems based on them (Calculus);
 define continuity of a function (Calculus);
 find the continuity of a given function from graphs and solve problems based on them (Calculus);
 define the derivative of a function (Calculus);
 define and use the standard derivative formula for finding the derivatives (Calculus);
 define the different derivative rules such as derivative of a constant, multiplication by a constant, power rule, sum rule, difference rule, product rule, quotient rule, reciprocal rule and the famous chain rule (Calculus);
 find the derivatives of functions using the different derivative rules (Calculus);
 find derivatives of trigonometric functions (trigonometric derivatives) and solve problems based them (Calculus);
 find derivatives of exponential functions (exponential derivatives) and solve problems based on them (Calculus);
 find derivatives of logarithmic functions (logarithmic derivatives) and solve problems based on them (Calculus);
 define the positive and negative intervals of a function;
 find the positive and negative intervals from graphs;
 find the domain and range of radical and rational functions.
 There are no prerequisites for this course.
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 NonStandard 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 OneSided Limits (left hand and right hand limits, learn to Find OneSided 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.
 Math Majors.
 Engineering Majors.
 Working Professionals.
 Anybody interested in learning Functions (Pre Calculus), Trigonometry and Calculus 1.