CHAPTER 1 SEQUENCES
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A) REAL NUMBER SEQUENCES
B) ARITHMETIC SEQUENCES
C) GEOMETRIC SEQUENCES
D) SUMMATION NOTATION
E) MULTIPLICATION NOTATION
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CHAPTER 2 LIMIT OF FUNCTIONS
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A) FUNCTIONS (review)
1) Domain of a function
2) Zeros, Period and 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
B) LIMIT OF FUNCTIONS
1) Definition of Limit of a Function,
2) Limits on a graph
3) One-sided limits,
4) Limits involving Infinity
a) Checking from left and right
b) 0/a & a/0 ( zero over a number & a number over zero ) Video 1 ,
C) INDETERMINATE FORMS
1) 0/0 as a limit with algebraic expressions Video 1 ,
2) 0/0 as a limit with trigonometric expressions
3) ∞/∞ as a limit with algebraic expressions (infinite/infinite)
4) 0*∞ as a limit with algebraic expressions (zero times infinite)
5) ∞ – ∞ as a limit with algebraic expressions (infinite minus infinite)
6) 1^∞ as a limit with algebraic expressions (one to the power of infinite)
D) CONTINUITY
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CHAPTER 3 DERIVATIVES & DIFFERENTIATION
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A) Definition of Derivative of a Function
B) Basic derivative rules
1) Chain Rule for Composite Function
2) Definition of Derivative of Inverse Function,
3) Higher Order Derivative
C) DERIVATIVES OF ELEMENTARY FUNCTION
1) DERIVATIVES OF EXPONENTIAL FUNCTIONS
2) DERIVATIVES OF LOGARITHMIC FUNCTIONS
- Logarithmic Differentiation Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 ,
3) DERIVATIVES OF TRIGONOMETRIC FUNCTIONS Video 1 , Video 2 , Video 3 , Video 4 , watch after 11min Video 5 , watch after 19min Video 6 , Video 7 , Video 8 , Video 9 , Video 10
4) DERIVATIVES OF ABSOLUTE VALUE FUNCTIONS Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 ,
5) IMPLICIT DIFFERENTIATION Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , Video 13 ,
6) DERIVATIVE OF PARAMETRIC FUNCTIONS Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , Video 13 , Video 14 ,
D) APPLICATIONS OF FIRST DERIVATIVE
1) L’Hopital’s Rule Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , Video 13 ,
2) Applications of First Derivative
-INTERVALS OF INCREASE AND DECREASE Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 ,
-MAXIMUM AND MINIMUM VALUES
- Absolute and Local Maximum Minimum Video 1 ,
- Finding Local Extrema
The Critical Points Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 ,
- The First Derivative Test Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , Video 13 , Video 14 , Video 15 , Video 16 , Video 20 ,
- Finding Absolute Extrema Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 ,
- Optimization Problems Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , Video 13 , Video 14 , Video 15 , Video 16 , Video 17 , Video 18 ,
E) APPLICATIONS OF SECOND DERIVATIVE
1) Concavity & Inflection Points Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , Video 13 , Video 14 , Video 15 ,
2) Second Derivative Test Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 ,
F) PLOTTING GRAPHS
1) Asymptotes ( Vertical, Horizontal, Oblique) Video 1(V) , Video 2(H) , Video 3(H) , Video 4(O) , Video 5(O) , Video 6(V) , Video 7(H) , Video 8(H) , Video 9(V AND H) , Video 10(ALL) , Video 11(ALL) , Video 12 , Video 13 ,
2) Curve Plotting Vid 0 , Vid 1 , Vid 2 , Vid 3 , Vid 4 , Vid 5 , Vid 6 , Vid 7 , Vid 8 , Vid 9 , Vid 10 , Vid 11 , Vid 12 , Vid 13 , Vid 14 , Vid 15 , Vid 16 , Vid 17 , Vid 18 , Vid 19 , Vid 20 , Vid 21 , Vid 22 , Vid 23 (very good playlist),
CHAPTER 4 INTEGRAL
A) INDEFINITE INTEGRAL
A) DEFINITION OF THE INDEFINITE INTEGRAL Vid 1 , Vid 2 , Vid 3 , Vid 4 , Vid 5 , Vid 6 , Vid 7 ,
B) PROPERTIES OF THE INDEFINITE INTEGRAL
C) BASIC INTEGRATION FORMULAS Vid 1 , Vid 2 , Vid 3 , Vid 4 , Vid 5 , Vid 6 , Vid 7 , Vid 8 , Vid 9 , Vid 10 , Vid 11 , Vid 12 , Vid 13 , (exponential) Vid 14 , (exponential) Vid 15 , (exponential) Vid 16 , (logarithmic) Vid 17 , (logarithmic) Vid 18 , (logarithmic) Vid 19 , (trig) Vid 20 , (trig) Vid 21 , Vid 22 , Vid 22 , Vid 23 , Vid 24 ,
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B) INTEGRATION METHODS
A) INTEGRATION BY SUBSTITUTION Vid 1 , Vid 2 , Vid 3 , Vid 4 , Vid 5 , Vid 6 , Vid 7 , Vid 8 , Vid 9 , Vid 10 , Vid 11 , Vid 12 (nice playlist 13 examples),
B) INTEGRATION BY PARTS Vid 1 , Vid 2 , Vid 3 , Vid 4 , Vid 5 , Vid 6 , Vid 7 , Vid 8 , Vid 9 , Vid 10 ,
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)&& Vid 1 , Vid 2 , Vid 3 ,
2) Using Partial Fractions Vid 1 , Vid 2 , Vid 3 , Vid 4 , Vid 5 (first 2 examples), Vid 6 , Vid 7 , Vid 8 , Vid 9 (long complete lesson), Vid 10 (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 vid 1 ,
C) DEFINITE INTEGRALS
D) APPLICATIONS OF DEFINITE INTEGRAL
1) Finding the area under a curve,
2) Calculating the volume of a solid of revolution,
3) Finding the length of a curve,
4) Calculating the area of a surface of revolution,
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CHAPTER 5 COMPLEX NUMBERS
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A) Imaginary Unit,
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– Powers of the Imaginary Unit,
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B) Complex Numbers,
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– Equations with Imaginary Root,
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C) Complex Plane
1) Conjugate of a Complex Number,
2) Basic operations in C,
3) Modulus of a Complex Number,
4) Distance Between Two Complex Numbers
D) Polar Coordinate Systems
1) Relation Between Polar and Rectangular Coordinate Systems,
2) Polar Form of a Complex Number
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CHAPTER 6 VECTORS AND ANALYTIC GEOMETRY IN SPACE
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A) Coordinates in Space
1) Distance Between Two Points,
2) Equation of Sphere
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B) Vectors in Space
1) Vector operations,Addition, Subtraction, Multiplication with Scalar
2) Linear Independence,Parallel Vectors
3) Dot Product, The Angle Between Two Vectors
4) Cross Product
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CHAPTER 7 CONIC SECTIONS
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A) Ellipse
1) Basic elements of an ellipse,
2) Equation of an ellipse
3) Position of a line and an ellipse,
4) The tangent and secant line to an ellipse,
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B) Hyperbola
1) Basic elements of a hyperbola,
2) Equation of an a hyperbola,
3) Position of a line and a hyperbola,
4) The tangent and secant line to a hyperbola,
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C) Parabola
1) Basic elements of a parabola,
2) Equation of a parabola,
3) Position of a line and a parabola
4) The tangent and secant line to a parabola
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CHAPTER X
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A)
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B)
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C)
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1)
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5)
6)
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b)
c)
d)
e)
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a Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , Video 13 , Video 14 , Video 15 , Video 16 , Video 17 , Video 18 , Video 19 , Video 20 ,
a Vid 1 , Vid 2 , Vid 3 , Vid 4 , Vid 5 , Vid 6 , Vid 7 , Vid 8 , Vid 9 , Vid 10 , Vid 11 , Vid 12 , Vid 13 , Vid 14 , Vid 15 , Vid 16 , Vid 17 , Vid 18 , Vid 19 , Vid 20 ,