12th+Introduction+to+Calculus

=Semester 1:=
 * Text: Saxon //Advanced Mathematics//, Second Edition**


 * Quarter 1**


 * Lesson 1** Geometry Review
 * Lesson 2** More on Area * Cylinders and Prisms * Cones and Pyramids * Spheres
 * Lesson 3** Pythagorean Theorem * Triangle Inequalities (1) * Similar Polygons * Similar Triangles
 * Lesson 4** Construction
 * Lesson 5** Exponents and Radicals * Complex Numbers * Areas of Similar Geometric Figures * Diagonals of Rectangular Solids
 * Lesson 6** Fractional Equations * Radical Equations * Systems of Three Linear Equations
 * Lesson 7** Inductive and Deductive Reasoning * Logic * The Contrapositive * Converse and Inverse
 * Lesson 8** Statements of Similarity * Proportional Segments * Angle Bisectors and Side Ratios
 * Lesson 9** Congruent Figures * Proof Outlines
 * Lesson 10** Equation of a Line * Rational Denominators * Completing the Square
 * Lesson 11** Circles * Properties of Circles * The Quadratic Formula
 * Lesson 12** Angles and Diagonals in Polygons * Proof of the Chord-Tangent Theorem
 * Lesson 13** Intersecting Secants * Intersecting Secants and Tangents * Products of Chord Segments * Products of Secant and Tangent Segments
 * Lesson 14** Sine, Cosine, and Tangent * Angles of Elevation and Depression * Rectangular and Polar Coordinates * Coordinate Conversion
 * Lesson 15** Assumptions * Proofs
 * Lesson 16** Complex Fractions * Abstract Equations * Division of Polynomials
 * Lesson 17** Proofs of the Pythagorean Theorem * Proofs of Similarity
 * Lesson 18** Advanced Word Problems
 * Lesson 19** Nonlinear Systems * Factoring Exponentials * Sum and Difference of Two Cubes
 * Lesson 20** Two Special Triangles
 * Lesson 21** Evaluating Functions * Domain and Range * Types of Functions * Tests for Functions

Quarter 2

 * Lesson 22** Absolute Value * Reciprocal Functions
 * Lesson 23** The Exponential Function * Sketching Exponentials
 * Lesson 24** Sums of Trigonometric Functions * Combining Functions
 * Lesson 25** Age Problems * Rate Problems
 * Lesson 26** The Logarithmic Form of the Exponential * Logarithmic Equations
 * Lesson 27** Related Angles * Signs of Trigonometric Functions
 * Lesson 28** Factorial Notation * Abstract Rate Problems
 * Lesson 29** The Unit Circle * Very Large and Very Small Fractions * Quadrantal Angles
 * Lesson 30** Addition of Vectors * Overlapping Triangles
 * Lesson 31** Symmetry * Reflections * Translations
 * Lesson 32** Inverse Functions * Four Quadrant Signs * Inverse Trigonometric Functions
 * Lesson 33** Quadrilaterals * Properties of Parallelograms * Types of Parallelograms * Conditions for Parallelograms * Trapezoids
 * Lesson 34** Summation Notation * Linear Regression * Decomposing Functions
 * Lesson 35** Change in Coordinates * The Name of a Number * The Distance Formula
 * Lesson 36** Angles Greater Than 360° * Sums of Trigonometric Functions * Boat-in-the-River Problems
 * Lesson 37** The Line as a Locus * The Midpoint Formula
 * Lesson 38** Fundamental Counting Principle and Permutations * Designated Roots * Overall Average Rate **Lesson 39** Radian Measure of Angles * Forms of Linear Equations
 * Lesson 40** The Argument in Mathematics * The Laws of Logarithms * Properties of Inverse Functions
 * Lesson 41** Reciprocal Trigonometric Functions * Permutation Notation
 * Lesson 42** Conic Sections * Circles * Constants in Exponential Functions
 * Lesson 43** Periodic Functions * Graphs of Sin and Cos
 * Lesson 44** Abstract Rate Problems
 * Lesson 45** Conditional Permutations * Two-Variable Analysis Using a Graphing Calculator
 * Lesson 46** Complex Roots * Factoring Over the Complex Numbers
 * Lesson 47** Vertical Sinusoid Translations * Arctan
 * Lesson 48** Powers of Trigonometric Functions * Perpendicular Bisectors
 * Lesson 49** The Logarithmic Function * Development of the Rules for Logarithms
 * Lesson 50** Trigonometric Equations

=Semester 2:= Textbook: The Mooculus Textbook Written by Jim Fowler, and Bart Snapp, Professors at Ohio State University

Topics Covered Spring 2014:

0 - Functions 1 - Limits 2 - Infinity and Continuity 3 - Basics of Derivatives 4 - Curve Sketching 5 - The Product Rule and Quotient Rule 6 - The Chain Rule 8 - Applications of Differentiation
 * One-to-one functions
 * Inverse functions
 * The definition of a limit
 * Limit laws
 * Infinite limits
 * Limits at infinity
 * Continuity
 * Slope of a tangent line via limits
 * Basic derivative rules
 * Extrema
 * The first derivative test
 * Concavity and inflection points
 * The second derivative test
 * Sketching the plot of a function
 * The product rule
 * The quotient rule
 * The chain rule
 * Implicit differentiation
 * Logarithmic differentiation
 * L'Hôpital's Rule
 * The derivative as a rate
 * Rated rates problems