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which chapters to focus on in calculus?

Discussion in 'PCAT Discussions' started by dmd20000, Dec 15, 2008.

  1. dmd20000

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  3. dmd20000

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    there are 15 chapters in this book. here is the the breakdown for each chapter below. let me know which chapters are important. thanks


    • 1. Preparation for Calculus1.1 Graphs and Models1.2 Linear Models and Rates of Change1.3 Functions and Their Graphs1.4 Fitting Models to Data1.5 Inverse Functions1.6 Exponential and Logarithmic Functions
    • 2. Limits and Their Properties2.1 A Preview of Calculus2.2 Finding Limits Graphically and Numerically2.3 Evaluating Limits Analytically2.4 Continuity and One-Sided Limits2.5 Infinite LimitsSection Project: Graphs and Limits of Trigonometric Functions
    • 3. Differentiation3.1 The Derivative and the Tangent Line Problem3.2 Basic Differentiation Rules and Rates of Change3.3 Product and Quotient Rules and Higher–Order Derivatives3.4 The Chain Rule3.5 Implicit DifferentiationSection Project: Optical Illusions3.6 Derivatives of Inverse Functions3.7 Related Rates3.8 Newton's Method
    • 4. Applications of Differentiation4.1 Extrema on an Interval4.2 Rolle's Theorem and the Mean Value Theorem4.3 Increasing and Decreasing Functions and the First Derivative TestSection Project: Rainbows4.4 Concavity and the Second Derivative Test4.5 Limits at Infinity4.6 A Summary of Curve Sketching4.7 Optimization ProblemsSection Project: Connecticut River4.8 Differentials
    • 5. Integration5.1 Antiderivatives and Indefinite Integration5.2 Area5.3 Riemann Sums and Definite Integrals5.4 The Fundamental Theorem of CalculusSection Project: Demonstrating the Fundamental Theorem5.5 Integration bySubstitution5.6 Numerical Integration5.7 The Natural Logarithmic Function: Integration5.8 Inverse Trigonometric Functions: Integration5.9 Hyperbolic FunctionsSection Project: St. Louis Arch
    • 6. Differential Equations6.1 Slope Fields and Euler's Method6.4 Differential Equations: Growth and Decay6.5 Differential Equations: Separation of Variables6.4 The Logistic Equation6.5 First–Order Linear Differential EquationsSection Project: Weight Loss6.6 Predator–Prey Differential Equations
    • 7. Applications of Integration7.1 Area of a Region Between Two Curves7.2 Volume: The Disk Method7.3 Volume: The Shell MethodSection Project: Saturn7.4 Arc Length and Surfaces of Revolution7.5 WorkSection Project: Tidal Energy7.6 Moments, Centers of Mass, and Centroids7.7 Fluid Pressure and Fluid Force
    • 8. Integration Techniques, L'Hôpital's Rule, and Improper Integrals8.1 Basic Integration Rules8.2 Integration by Parts8.3 Trigonometric IntegralsSection Project: Power Lines8.4 Trigonometric Substitution8.5 Partial Fractions8.6 Integration by Tables and Other Integration Techniques8.7 Indeterminate Forms and L'Hôpital's Rule8.8 Improper Integrals
    • 9. Infinite Series9.1 Sequences9.2 Series and ConvergenceSection Project: Cantor's Disappearing Table9.3 The Integral Test and p–SeriesSection Project: The Harmonic Series9.4 Comparisons of SeriesSection Project: Solera Method9.5 Alternating Series9.6 The Ratio and Root Tests9.7 Taylor Polynomials and Approximations9.8 Power Series9.9 Representation of Functions by Power Series9.10 Taylor and Maclaurin Series
    • 10. Conics, Parametric Equations, and Polar Coordinates10.1 Conics and Calculus10.2 Plane Curves and Parametric EquationsSection Projects: Cycloids10.3 Parametric Equations and Calculus10.4 Polar Coordinates and Polar GraphsSection Project: Anamorphic Art10.5 Area and Arc Length in Polar Coordinates10.6 Polar Equations of Conics and Kepler's Laws
    • 11. Vectors and the Geometry of Space11.1 Vectors in the Plane11.2 Space Coordinates and Vectors in Space11.3 The Dot Product of Two Vectors11.4 The Cross Product of Two Vectors in Space11.5 Lines and Planes in SpaceSection Project: Distances in Space11.6 Surfaces in Space11.7 Cylindrical and Spherical Coordinates
    • 12. Vector–Valued Functions12.1 Vector–Valued FunctionsSection Project: Witch of Agnesi12.2 Differentiation and Integration of Vector–Valued Functions12.3 Velocity and Acceleration12.4 Tangent Vectors and Normal Vectors12.5 Arc Length and Curvature
    • 13. Functions of Several Variables13.1 Introduction to Functions of Several Variables13.2 Limits and Continuity13.3 Partial DerivativesSection Project: Moire Fringes13.4 Differentials13.5 Chain Rules for Functions of Several Variables13.6 Directional Derivatives and Gradients13.7 Tangent Planes and Normal LinesSection Project: Wildflowers13.8 Extrema of Functions of Two Variables13.9 Applications of Extrema of Functions of Two VariablesSection Project: Building a Pipeline13.10 Lagrange Multipliers
    • 14. Multiple Integration14.1 Iterated Integrals and Area in the Plane14.2 Double Integrals and Volume14.3 Change of Variables: Polar Coordinates14.4 Center of Mass and Moments of InertiaSection Project: Center of Pressure on a Sail14.5 Surface AreaSection Project: Capillary Action14.6 Triple Integrals and Applications14.7 Triple Integrals in Cylindrical and Spherical CoordinatesSection Project: Wrinkled and Bumpy Spheres14.8 Change of Variables: Jacobians
    • 15. Vector Analysis15.1 Vector Fields15.2 Line Integrals15.3 Conservative Vector Fields and Independence of Path15.4 Green's TheoremSection Project: Hyperbolic and Trigonometric Functions15.5 Parametric Surfaces15.6 Surface IntegralsSection Project: Hyperboloid of One Sheet15.7 Divergence Theorem15.8 Stoke's TheoremSection Project: The Planimeter
     
  4. ffpickle

    ffpickle Thread Killer
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    Chapters 1-6, 8.1,8.2,9.1,9.2 is a *very* comprehensive review. Don't forget there is non-calculus math on the PCAT.
     
  5. SHC1984

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    Kaplan book has 5 chapters on Math...is that a good review? I made A in Cal I, II and III but that was a LONG time ago...haha...so not sure if Kaplan review will be good enough for PCAT.
     
  6. ffpickle

    ffpickle Thread Killer
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    i don't know what kaplan's book covers, but if you got As in those courses, just as long as your brush up (i.e. study quite a bit), you should be fine. I saw a Kaplan book from a few yrs ago and their math section was abysmal. I can't imagine it has improved enough for the purposes of the PCAT. Do Hartcourt's test and you will get a good idea about what the math section is like.
     
  7. WhiteSnows

    WhiteSnows Think Right and Grow Rich
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    Pcat is an unpredictable test. They change the test questions oftenly, perhap every test. You should study everything since there are only 15 chapters. I had 36 chapters in microbiology and I had to learn everything.
     
  8. IrishOats

    IrishOats Go Pioneers!
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    Know the basic first and second derivatives and their rules. Know about points of inflection and concavity - how to find them, what they mean, etc. Know your very basic integrals. That should have you covered. Probably were about 5 to 8 calculus questions that I remember clearly.
    From your description of the chapters I'd recommend focusing on chapters 1 through 5.

    (Took PCAT August 2008, 87 percentile in Quantitative Ability)
     
    #7 IrishOats, Dec 21, 2008
    Last edited: Dec 21, 2008

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