Course Description
This course is a gateway to Calculus and it provides you with all the knowledge and skills you need in Calculus.
The course includes:
The course comprises 5 units and 30 lessons
Over 13 hours of video-lessons!
Each lesson includes a video lecture, a worksheet, a worksheet review video and an online quiz.
30 video lectures
30 worksheets
30 worksheet review videos with every question solved step-by step by the instructor
30 online quizzes
3 unit tests (on paper)
1 final exam (on paper)
an exclusive Getting Ready for Calculus unit where we introduce the difference quotient and limits!
COURSE GOALS
Upon course completion, you will learn how to:
- work with trigonometric functions
- sketch graphs of trigonometric functions
- solve trigonometric equations
- simplify trigonometric expressions and prove trigonometric identities
- use laws and formulas from trigonometry in solving triangles
- apply trigonometric to real life situations
- work with Cartesian and polar coordinates
- work with complex numbers
- use de Moivre's theorem to find powers and roots of complex numbers
- work with vectors in Cartesian and polar coordinates
- prove mathematical statements using mathematical induction
- apply the Fundamental Theorem of Algebra
- perform operations on matrices
- solve a system of linear equations using Gaussian elimination and Gauss-Jordan elimination
- find the difference quotient of a function
- calculate some elementary limits and read limits from graphs
TARGET AUDIENCE
This video-course is primarily intended for 12th grade students who would like to solidify their mathematical skills and knowledge before they take Calculus.
COURSE REQUIREMENTS
Students taking this course will need to have completed Algebra I, Math for 11th grade or an equivalent Math course prior to enrolling in this course.
UNIT 1 TRIGONOMETRY
Angles Measured in Radians or Degrees
Introducing Sine and Cosine
The Pythagorean Identity
Proving Other Trigonometric Identities
Graphing Trigonometric Functions
Tangent and Cotangent Functions
Secant and Cosecant Functions,
Tangent and Slope
Addition Formulas for Sine and Cosine
Half-Angle and Double Angle Formulas
Right Triangle Trigonometry
The Area of a Triangle
The Law of Sines and the Law of Cosines
Applications of Trigonometry
UNIT 2 COMPLEX NUMBERS AND POLAR FORM
Polar Form
Converting Points
Complex Numbers
The Arithmetic of Complex Numbers
De Moivre’s Theorem
Vectors in Cartesian and Polar Coordinates
UNIT 3 PROOF BY MATHEMATICAL INDUCTION AND THE FUNDAMENTAL THEOREM OF ALGEBRA
Proofs by Mathematical Induction
The Fundamental Theorem of Algebra
UNIT 4 LINEAR ALGEBRA
Introduction to Linear Algebra and Matrices
Row Echelon Form and Reduced Row Echelon Form
Coefficient Matrices
Gaussian Elimination and Gauss-Jordan Elimination
Matrix Addition and Matrix Multiplication
UNIT 5 GETTING READY FOR CALCULUS
Trigonometric Equations
The Difference Quotient
Introduction to Limits
