Calculus for dummies - Info and Reading Options

"Calculus for dummies" Table Of Contents:

• 1- pt. I. An overview of calculus
• 2- 1. What is calculus?
• 3- 2. The two big ideas of calculus : differentiation and integration
• 4- Slope
• 5- Rate
• 6- Plus infinite series
• 7- Divergent series
• 8- Convergent series
• 9- 3. Why calculus works
• 10- The limit concept : a mathematical microscope
• 11- Precision
• 12- Infinity
• 13- pt. II. Warming up with calculus prerequisites
• 14- 4. Pre-algebra and algebra review
• 15- Fractions
• 16- Multiplying fractions
• 17- Dividing fractions
• 18- Adding fractions
• 19- Subtracting fractions
• 20- Canceling in fractions
• 21- Absolute value
• 22- Powers
• 23- Roots
• 24- Simplifying roots
• 25- Logarithms
• 26- Factoring
• 27- GCF
• 28- Trinomial factoring
• 29- Solving quadratic equations
• 30- Factoring
• 31- The quadratic formula
• 32- Completing the square
• 33- 5. Funky functions and their groovy graphs
• 34- Independent and dependent variables
• 35- Function notation
• 36- Composite functions
• 37- Common functions and their graphs
• 38- Lines in the plane
• 39- Parabolic and absolute value functions
• 40- Couple oddball functions
• 41- Exponential functions
• 42- Logarithmic functions
• 43- Inverse functions
• 44- Horizontal transformations
• 45- Vertical transformations
• 46- 6. The trig tango
• 47- Right triangles
• 48- Unit circle
• 49- Measuring angles with radians
• 50- Hypotenuse
• 51- Graphing sine, cosine, and tangent
• 52- Inverse trig functions
• 53- Trig identities
• 54- pt. III. Limits
• 55- 7. Limits and continuity
• 56- One-sided limits
• 57- Limits and vertical asymptotes
• 58- Limits and horizontal asymptotes
• 59- Calculating instantaneous speed with limits
• 60- Linking limits and continuity
• 61- 8. Evaluating limits
• 62- Figuring a limit with your calculator
• 63- Solving limit problems with algebra
• 64- Evaluating limits at infinity
• 65- Limits at infinity and horizontal asymptotes
• 66- Solving limits at infinity with a calculator
• 67- Solving limits at infinity with algebra
• 68- pt. IV. Differentiation
• 69- 9. Differentiation orientation
• 70- The slope off a line
• 71- The derivative of a line
• 72- The derivative : it's just a rate
• 73- Calculus on the playground
• 74- Speed
• 75- The rate-slope connection
• 76- The derivative of a curve
• 77- The difference quotient
• 78- Average rate and instantaneous rate
• 79- 10. Differentiation rules : yeah, man, it rules
• 80- Basic differentiation rules
• 81- The constant rule
• 82- The power rule
• 83- The constant multiple rule
• 84- The sum rule
• 85- The difference rule
• 86- Differentiating trig functions
• 87- Differentiating exponential and logarithmic functions
• 88- The product rule
• 89- The quotient rule
• 90- The chain rule
• 91- Differentiating implicitly
• 92- Logarithmic differentiation
• 93- Differentiating inverse functions
• 94- Higher order derivatives
• 95- 11. Differentiation and the shape of curves
• 96- Positive and negative slopes
• 97- Concavity and inflection points
• 98- A local minimum
• 99- The absolute maximum
• 100- Finding local extrema
• 101- Critical numbers
• 102- Finding absolute extrema on a closed interval
• 103- Finding absolute extrema over a function's entire domain
• 104- Locating concavity and inflection points
• 105- Graphs of derivatives
• 106- The mean value theorem
• 107- 12. Your problems are solved : differentiation to the rescue!
• 108- Optimization problems
• 109- Maximum volume of a box
• 110- Maximum area of a corral
• 111- Position, velocity, and acceleration
• 112- Velocity, speed and acceleration
• 113- Maximum and minimum height
• 114- Velocity and displacement
• 115- Speed and distance traveled
• 116- Related rates
• 117- 13. More differentiation problems : going off on a tangent
• 118- Tangents and normals
• 119- The tangent line problem
• 120- The normal line problem
• 121- Linear approximations
• 122- Business and economics problems
• 123- Managing marginals in economics
• 124- pt. V. Integration and infinite series
• 125- 14. Intro to integration and approximating area
• 126- Integration : just fancy addition
• 127- Finding the area under a curve
• 128- Approximating area
• 129- Left sums
• 130- Right sums
• 131- Midpoint sums
• 132- Summation notation
• 133- Riemann sums with sigma notation
• 134- Finding exact area with the definite integral
• 135- Trapezoid rule and Simpson's rule (Thomas Simpson 1710-1761)
• 136- 15. Integration : it's backwards differentiation
• 137- Antidifferentiation
• 138- Area function
• 139- Fundamental theorem of calculus
• 140- Antiderivatives
• 141- Finding area with substitution problems
• 142- 16. Integration techniques for experts
• 143- Integration by parts
• 144- Trig integrals
• 145- Integrals containing sines and cosines
• 146- Integrals containing secants and tangents or cosecants
• 147- Trigonometric substitution
• 148- Partial fractions
• 149- 17. Forget Dr. Phil : use the integral to solve problems
• 150- The mean value theorem for integrals and average value
• 151- The area between two curves
• 152- Finding the volumes of weird solids
• 153- Analyzing arc length
• 154- Surfaces of revolution
• 155- 18. Taming the infinite with improper integrals
• 156- L/Hôpital's rule
• 157- Improper integrals
• 158- Improper integrals with vertical asymptotes
• 159- Improper integrals with one or two infinite limits of integration
• 160- 19. Infinite series
• 161- Sequences and series
• 162- Stringing sequences
• 163- Summing series
• 164- Convergence or divergence
• 165- Alternating series
• 166- pt. VI. The part of tens
• 167- 20. Ten things to remember
• 168- The product rule
• 169- The quotient rule
• 170- 21. Ten things to forget
• 171- 22. Ten things you can't get away with.

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