CHAPTER 1 ANALYTIC GEOMETRY
Part1: ANALYTIC ANALYSIS OF POINTS AND LINES
1) ANALYTIC ANALYSIS OF POINTS
a) The Distance Between Two Points
b) The Midpoint of a Line Segment
c) Dividing a Line Segment in a Given Ratio
2) ANALYTIC ANALYSIS OF TRIANGLES
a) The Centroid of Triangle
b) The Area of Triangle
3) SLOPE OF A LINE
a) Slope of a Line
b) Finding the Slope of a Line
c) Parallel and Perpendicular Lines
4) EQUATION OF A LINE
–Equation of a line in Point-Slope Form
–Equation of a Line Parallel to Coordinate Axis
5) FINDING THE SLOPE OF A LINE WITH A GIVEN EQUATION
6) RELATIVE POSITION OF TWO LINES
7) ANGLES BETWEEN TWO LINES
8) DISTANCE FROM A POINT TO A LINE
9) DISTANCE BETWEEN TWO PARALLEL LINES
10) SYMMETRY OF A LINE WITH RESPECT TO PARALLEL
Part2: ANALYTIC ANALYSIS OF CIRCLES
1) STANDARD EQUATION OF A CIRCLE
2) EQUATIONS OF A CIRCLE WHICH IS TANGENT TO AN AXIS
3) GENERAL EQUATION OF A CIRCLE
–General 2nd degree equation
4) RELATIVE POSITION OF A LINE AND A CIRCLE
5) EQUATIONS OF TANGENT AND NORMAL LINES
– Equations of Tangents Drawn from an External Point
CHAPTER 2 FUNCTIONS
1) DOMAIN OF A FUNCTION
a) Polynomial Functions
b) Rational Functions
c) Radical Functions
d) Exponential Functions
e) Logarithmic Functions
f) Mixed Cases
2) ZEROS, PERIOD AND EXTREME VALUES
a) Zeros
b) Period
c) Extreme Values
3) COMPOSITE FUNCTION
4) INVERSE OF A FUNCTION
5) CONSTANT,INCREASING AND DECREASING
6) EVEN AND ODD FUNCTIONS
7) PIECEWISE FUNCTION
8) ABSOLUTE VALUE FUNCTION
CHAPTER 3 SEQUENCES
1) REAL NUMBER SEQUENCES
A) Criteria for the Existence of a Sequence
B) Types of Sequences
1) Finite and Infinite Sequences
2) Monotone Sequences
3) Piecewise Sequences
4) Recursively Defined Sequences
2) ARITHMETIC SEQUENCES
General Term of an Arithmetic Sequence
Number of Terms of an Arithmetic Sequence
Advanced General Term of an Arithmetic Sequence
Middle Term of an Arithmetic Sequence
Sum of Terms of an Arithmetic Sequence
Alternative Sum Formula of an Arithmetic Sequence
3) GEOMETRIC SEQUENCES
Arithmetic and Geometric Growth
General Term of a Geometric Sequence
Advanced General Term of a Geometric Sequence
Middle Term of a Geometric Sequence
Sum of Terms of a Geometric Sequence
The Infinite Sum of a Geometric Sequence
4) SUMMATION NOTATION
5) MULTIPLICATION NOTATION
CHAPTER 4 LIMITS
1) LIMIT OF FUNCTIONS
A) DEFINITION OF LIMIT OF A FUNCTION
B) LIMITS ON A GRAPH
C) ONE-SIDED LIMITS
D) LIMITS OF SPECIAL FUNCTIONS
E) LIMITS INVOLVING INFINITY
1) Checking from left and right
2) 0/a & a/0 ( zero over a number & a number over zero )
2) INDETERMINATE FORMS
A) 0/0 AS A LIMIT WITH ALGEBRAIC EXPRESSIONS
B) 0/0 AS A LIMIT WITH TRIGONOMETRIC EXPRESSIONS
C) ∞/∞ AS A LIMIT WITH ALGEBRAIC EXPRESSIONS (INFINITE/INFINITE)
D) 0*∞ AS A LIMIT WITH ALGEBRAIC EXPRESSIONS (ZERO TIMES INFINITE)
E) ∞ – ∞ AS A LIMIT WITH ALGEBRAIC EXPRESSIONS (INFINITE MINUS INFINITE)
F) 1^∞ AS A LIMIT WITH ALGEBRAIC EXPRESSIONS (ONE TO THE POWER OF INFINITE)
3) CONTINUITY
CHAPTER 5 DERIVATIVES & DIFFERENTIATION
1) DEFINITION OF DERIVATIVE OF A FUNCTION
2) BASIC DERIVATIVE RULES
A) CHAIN RULE FOR COMPOSITE FUNCTION
B) DEFINITION OF DERIVATIVE OF INVERSE FUNCTION,
C) HIGHER ORDER DERIVATIVE
3) DERIVATIVES OF ELEMENTARY FUNCTION
A) DERIVATIVES OF EXPONENTIAL FUNCTIONS
B) DERIVATIVES OF LOGARITHMIC FUNCTIONS
– Logarithmic Differentiation,
C) DERIVATIVES OF TRIGONOMETRIC FUNCTIONS , watch after 11min, watch after 19min ,
D) DERIVATIVES OF ABSOLUTE VALUE FUNCTIONS 1 ,
E) IMPLICIT DIFFERENTIATION 1 ,
F) DERIVATIVE OF PARAMETRIC FUNCTIONS 1 ,
4) APPLICATIONS OF FIRST DERIVATIVE
A) L’HOPITAL’S RULE 1 , 1, V,
B) APPLICATIONS OF FIRST DERIVATIVE
1) Intervals Of Increase And Decrease,
2) Maximum And Minimum Values
– Absolute and Local Maximum Minimum,
– Finding Local Extrema
3) The Critical Points,
– The First Derivative Test ,
– Finding Absolute Extrema,
– Optimization Problems ,
5) APPLICATIONS OF SECOND DERIVATIVE
A) CONCAVITY & INFLECTION POINTS ,
B) SECOND DERIVATIVE TEST,
6) PLOTTING GRAPHS
A) ASYMPTOTES ( Vertical, Horizontal, Oblique)(V AND H) , (ALL) , (ALL) , ,
B) CURVE PLOTTING (very good playlist),
CHAPTER 6 INTEGRAL
1) INDEFINITE INTEGRAL
A) DEFINITION OF THE INDEFINITE INTEGRAL,
B) PROPERTIES OF THE INDEFINITE INTEGRAL
C) BASIC INTEGRATION FORMULAS (exponential) , (exponential), (exponential) , (logarithmic) , (logarithmic) Vid 18 , (logarithmic) , (trig) , (trig) .
2) INTEGRATION METHODS
A) INTEGRATION BY SUBSTITUTION (nice playlist 13 examples),
B) INTEGRATION BY PARTS
C) INTEGRATING PARTIAL FRACTIONS
1) Using Basic Derivative Rules
a) integral(1/u)du=ln IuI + c &&
b) integral(1/u(power-n))du=u(power-n+1)/(n+1) + c &&
c) integral(1/[1+u(power-2)])du= arctan (u) + c (Integration using completing the square : arctan)&&
2) Using Partial Fractions (first 2 examples), (long complete lesson), (nice playlist),
3) If the Degree of P(x) is Bigger than or Equal to the Degree of Q(x)
D) INTEGRATING SIMPLE RADICAL FUNCTIONS
E) INTEGRATING TRIGONOMETRIC FUNCTIONS
– general
3) DEFINITE INTEGRALS
4) APPLICATIONS OF DEFINITE INTEGRAL
A) FINDING THE AREA UNDER A CURVE,
B) CALCULATING THE VOLUME OF A SOLID OF REVOLUTION,
C) FINDING THE LENGTH OF A CURVE,
D) CALCULATING THE AREA OF A SURFACE OF REVOLUTION,
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VID1, VID2, VID3, VID4, VID5, VID6, VID7, VID8, VID9, VID10, VID11, VID12, VID13, VID14, VID15, VID16,