• Raison d'Maple
  •  Four Properties of Maple
  •  The Worksheet:  A handy place to solve problems.
  • Get to know the language
    • Problems:
  •  Experiment!
    • Problems

• An introduction to the Maple language
  •   Arithmetic
  •   Expressions, Names,  Statements, and Assignments
  •   Functions
  •   Built in Maple functions and Operations with Functions
  •   Using Maple as a fancy graphing calculator.
  •   Data types, Expression Sequences, Lists, Sets, Arrays, Tables:
  •   Maple control statements
  •   A Brief Vocabulary of Maple Words
  •   Trouble Shooting Notes

• Setting Up and Solving Problems
  • What is a problem?
  • Setup -- Solve -- Interpret
  • A Swimming Pool Problem:
  • Four methods of solving equations
  •  Problems
  •    More About Plotting
  •  Putting in a parameter.
  •   Problems
  •   Defining your own Maple words.
  •    Problems

•  More worked Problems
  • A billiard ball problem.
  • A Variation on the Billiard Ball Problem.
  • Water tank problem.
  • A ladder problem.
  • Another  Ladder Problem.
  • Variation on the last ladder problem.

•  Differentiation and its uses.
  •  Defining Derivatives
  • The student package
  • Problems
  • Newton's Method.
  • Use of the derivatives in plotting
  • Implicit Differentiation
  •  Max-min Problems
    • A Paper folding problem:

• More Max-min Problems
  •  Stumbling onto max-min Problems
  •  Problems:
  • Solutions

• Early Integration.
  •  Learning to use the Maple words  Sum  and  sum .
  •  Riemann  Sums with the student package
  • Learning  to use   Int and int.
  • Average value.
  •  Modeling the flow of air in lungs:
  • Two Area problems.

• Moments and Center of Mass
  • Center of mass of a Wire
  •  Center of mass of a solid of revolution

• Definitions and Theorems of Calculus I

• Inverse Functions
  •  A Useful Function  -- The natural logarithm
  • The inverse of the natural log
  •   Inverse Functions:  The inverse trig functions

•   Integration Techniques and Applications
  •  Symbolic Integration Problems
    •  A Substitution Problem:
    • An Integration by Parts Problem:
    • A Trig Substitution:
    • A Partial Fractions Problem
    •   Problems:
  •  Numerical Integration Problems
    • The Trapezoid Rule
    • Problems
    • Simpson's Rule.
    • More problems with Trapezoid and Simpson

•   Taylor's Theorem
  • Taylor polynomials
  • Taylor remainder theorem
  •  Problems

•   Sequences and Series
  • Sequences
    •  Periodic Points of functions.
    • Problems
  • Series
    • Problems
  •  Two interesting curves
    • The Snowflake Curve
    • A Spacefiller

• Differential equations
  • Terminology
  • Problems leading to first order equations
  • Logistic Growth

Index

•    if .. then .. elif .. else .. fi;
•  nops
•  plots[display]
•  unapply
• ?if
• @
• D operator
• DEtools
• Digits
• ERROR
• ETAIL
• IVP
• Int
• Integration by parts
• Integration by substitution
• Logistic growth
• NULL
• Newton's method
• Riemann Zeta function
• Riemann sum
• Riemann sum
• Simpson's rule
• Snowflake Curve
• Sum
• Taylor polynomial
• Taylor remainder
• Text  Cell
• approximate moment
• arithmetic sequence
• attracting fixed point
• center of mass
• center of mass
• change of variable
• converge   
• converges to a limit
• convert(..,polynom)
• critical points
• debug(something);
• dfieldplot
• diff
• differential equation
• dsolve
• error in Simpson's rule.     
• error in the trapezoid rule
• evalf    
• evalm
• example
• expand
• expression
• expressions.
• exprseq
• eyeball
• factor
• fixed points
• for .. from .. by .. to .. while .. do .. od;
• fsolve
• fundamental theorem of calculus
• geometric sequence
• geometric series
• if..then..fi
• implicit differentiation
• inflection points
• input cell
• int
• int
• interface(verboseproc=2);
• isocline
• law of radioactive decay
• leftsum and rightsum
• limit
• limit
• logarithm function
• lungs
• online Help
• op
• order of a differential equation
• output cell
• parameterization of the ellipse
• partial fractions decomposition
• piecewise
• plot
• plot
• plot3d
• plot3d
• plots
• plots[implicitplot]
• plots[polygonplot]
• printlevel
• proc
• repelling fixed point
• section
• separable equation
• seq
• sequence of iterates
• sequence of numbers
• series
• showtangent
• solid of revolution   
• student package
• student package
• student[middlesum]
• subs
• sum
• syntax
• taylor
• tilde
• trapezoid rule
• unapply
• unapply.
• whattype