MA5 Calculus I:
Calculus of a Single Variable (Parts 1 - 7)
with Herbert I. Gross (M.I.T.)
37 B/W videotapes
English
Complete 37 tape set - $3700
Individual videotape $110 ea.
Also available on DVDs, call for pricing

Calculus covers the material normally found in the first two years of a modern college sequence in calculus, differential equations, and linear algebra and is suitable for all students with the requisite background.

The course begins with elementary set theory and other aspects of the "new math" and continues with differential and integrated calculus, circular and transcendental functions, and infinite series. The course then introduces vector arithmetic and vector calculus, partial derivatives, matrix algebra, and multiple integration. The final part of the course covers complex variables, differential equations, and linear algebra.

The complete course includes: 37 black & white videotapes.

Please Note: For an accompanying Textbook please go to www.Amazon.com and search for George Brinton Thomas. You will find a selection of helpful books.

Part I - Sets, Functions, and Limits
Part II - Differentiation
Part III - The Circular Functions
Part IV - The Definite Integral
Part V - Transcendental Functions
Part VI - More Integration Techniques
Part VII - Infinite Series

Please see the following individual videotape descriptions for detailed information.

MA5-1 Calculus I: Calculus of a Single Variable - Part I: Sets, Functions, and Limits
with Herbert I. Gross (M.I.T.)
6 B/W videotapes
English
Complete 6 tape set - $600
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Analytic Geometry
Cartesian coordinates; curves as sets of points; graphs of functions; equations of straight lines; simultaneous linear equations.

Tape 2: Functions
Notations; concepts of onto and one-to-one; the arithmetic of functions of a real variable; intervals and
deleted neighborhoods; absolute values; composition of functions.

Tape 3: Inverse Functions
The concept of an inverse function; graphical interpretation; single-valued and multivalued functions;
branches of functions.

Tape 4: Derivatives and Limits
Instantaneous speed as an outgrowth of average speed; definition of limit; instantaneous speed as a limit;
the formal definition of limit and some consequences.

Tape 5: A More Rigorous Approach to Limits
A continuation of the previous lecture; important limit properties are developed as theorems from the formal
definition of limit.

Tape 6: Mathematical Induction
The meaning of mathematical induction; some examples of what mathematical induction is and isn't,
applications to limit theorems.

MA5-2 Calculus I: Calculus of a Single Variable
Part II: Differentiation
with Herbert I. Gross (M.I.T.)
11 B/W videotapes
English
Complete 11 tape set - $1100
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Derivatives of Some Simple Functions
Definition of derivative; the derivative of x to the n where n is an integer; derivatives of sums, differences,
products, and quotients.

Tape 2: Approximations and Infinitesimals
Approximating delta y by f(x) delta x; discussion of the difference between delta y and f(x) delta x;
introduction to the chain rule.

Tape 3: Composite Functions and the Chain Rule
Composition of functions; a graphical interpretation; applications to parametric equations; using the chain
rule to extend the concept of finding derivatives.

Tape 4: Differentiation of Inverse Functions
The concept of an inverse function; differentiation of an inverse function; when is a function invertible?

Tape 5: Implicit Differentiation
Finding the derivative when the functional relationship is implied; application to the case of x to the n where n
is a rational number; the use of implicit differentiation in the study of related rates.

Tape 6: Continuity
Physical interpretation of continuity; the definition of continuity in terms of limits; a geometric interpretation
of continuity; analytic consequences.

Tape 7: Curve Plotting
Basic pre-calculus review; even and odd functions and other symmetries; the role of the first and second
derivatives in curve plotting; stationary points; inflections.

Tape 8: Maxima and Minima
High and low points of a curve; techniques for finding them; applications to finding maxima and minima of
functions; physical applications.

Tape 9: Rolle's Theorem and its Consequences
Statement of Rolle's Theorem; a geometric interpretation; some cautions; the Mean Value Theorem;
consequences of the Mean Value Theorem.

Tape 10: Inverse Differentiation
The "opposite" of differentiation; trying to find f(x) knowing f(x); some examples; some formulas; notation.

Tape 11: The "Definite" Indefinite Integral
The meaning of the definite integral as g(b) - g(a) where g'(x) = f(x); some applications.

MA5-3 Calculus I: Calculus of a Single Variable
Part III: The Circular Functions
with Herbert I. Gross (M.I.T.)
2 B/W videotapes
English
Complete 2 tape set - $200
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Circular Functions
Trigonometric functions without angles; the logic of radian measure; definition of circular functions;
derivatives of sin x and cos x.

Tape 2: Inverse Circular Functions
Meaning of arc sin x in terms of the sine function; the derivative of arc sin x in terms of the derivative of
sin x; some applications.

MA5-4 Calculus I: Calculus of a Single Variable
Part IV: The Definite Integral
with Herbert I. Gross (M.I.T.)
4 B/W videotapes
English
Complete 4 tape set - $400
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: The Definite Integral
Axiomatic approach to area; area approximations by upper and lower bounds; the method of exhaustion;
using limits to find areas of nonrectilinear regions; piecewise continuity; trapezoidal approximations.

Tape 2: Marriage of Differential and Integral Calculus
First Fundamental Theorem of Integral Calculus; some applications; Second Fundamental Theorem of
Integral Calculus; some applications; significance of the two theorems.

Tape 3: Three-Dimensional Area
Extending the axioms of area to volume; some applications; the method of cylindrical shells.

Tape 4: One-Dimensional Area
The main difference between arc-length and either area or volume; the limit definition of arc-length;
approximating errors and their magnitude when we use infinite sums.

MA5-5 Calculus I: Calculus of a Single Variable
Part V: Transcendental Functions
with Herbert I. Gross (M.I.T.)
4 B/W videotapes
English
Complete 4 tape set - $400
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Logarithms without Exponents
The concept of the natural logarithm; the notion of the rate of change being proportional to the amount
present; the general concept of a logarithmic function; In x in terms of differential and integral calculus;
the meaning of the number e as the base of the natural logarithms.

Tape 2: Inverse Logarithms
The invertibility of the logarithmic function; e to the x as the inverse of In x; a discussion of exponential
functions; some applications.

Tape 3: What a Difference a Sign Makes
Hyperbolic functions; comparisons with circular functions; relationship between hyperbolic functions and
exponential functions; applications of calculus to hyperbolic functions.

Tape 4: Inverse Hyperbolic Functions
The theory of inverse functions applied to the hyperbolic functions; some formulas for differentiation and
integration; some applications.

MA5-6 Calculus I: Calculus of a Single Variable
Part VI: More Integration Techniques
with Herbert I. Gross (M.I.T.)
4 B/W videotapes
English
Complete 4 tape set - $400
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Come Basic Recipes
A review and extension of previous results for finding f(x) knowing f'(x); particular emphasis on the case
where f'(x) involves the sum and/or difference of two squares; completing the square.

Tape 2: Partial Fractions
The concept of partial fractions; finding f(x) when f'(x) is the quotient of two polynomials; some notes about
identities; application of partial fractions to the case where f is of the form f(sin x, cos x).

Tape 3: Integration by Parts
Using the identity d(uv) = udv + vdu to find the integral of udv knowing the integral of vdu; using the
technique to evaluate certain integrals; reduction formulas; some applications.

Tape 4: Improper Integrals
The problem of trying to study the integral of f(x)dx when f(x) is not continuous on the interval [a,b]; what
happens if the limits of integration are not finite; importance of improper integrals.

MA5-7 Calculus I: Calculus of a Single Variable
Part VII: Infinite Series
with Herbert I. Gross (M.I.T.)
6 B/W videotapes
English
Complete 6 tape set - $600
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Many versus Infinite
Discussion of how infinity differs from "very large"; some subtle and not-so-subtle consequences of the
difference; the case against intuition; motivating infinite series in terms of finding area as a limit.

Tape 2: Positive Series
The special case wherein each term in the series is non-negative; the concept of convergence; the comparison
test; the ratio test; the integral test.

Tape 3: Absolute Convergence
Non-absolute convergence; conditional and absolute convergence; a series converging when each of its
negative terms is replaced by the absolute value of that term; geometric interpretation.

Tape 4: Polynomial Approximations
Using an nth degree polynomial to approximate a function f(x); how to choose the coefficients; power series;
Taylor's Remainder Theorem; expressing functions in terms of power series.

Tape 5: Uniform Convergence
Pointwise convergence versus uniform convergence; some important consequences of uniform convergence;
applications of uniform convergence to the study of power series.

Tape 6: Uniform Convergence of Power Series
Weirstrass M-test; using power series to evaluate definite integrals when we do not know the antiderivative
of the integrand.

The complete course includes: 26 black & white videotapes.

Please Note: For an accompanying Textbook please go to www.Amazon.com and search for George Brinton Thomas. You will find a selection of helpful books..

Part I - Vector Arithmetic
Part II - Vector Calculus
Part III - Partial Derivatives
Part IV - Matrix Algebra
Part V - Multiple Integration

Please see the following for individual videotape titles.

MA6-1  Calculus II: Calculus of Several Variables
Part I: Vector Arithmetic
with Herbert I. Gross (M.I.T.)
6 B/W videotapes
English
Complete 6 tape set - $600
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: The "Game" of Mathematics
Tape 2: "Arrow" Arithmetic
Tape 3: Three-Dimensional Vectors
Tape 4: The Dot Product
Tape 5: The Cross Product
Tape 6: Equations of Lines and Planes

MA6-2 Calculus II: Calculus of Several Variables
Part II: Vector Calculus
with Herbert I. Gross (M.I.T.)
4 B/W videotapes
English
Complete 4 tape set - $400
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Vector Functions of a Scalar Variable
Tape 2: Tangential and Normal Vectors
Tape 3: Polar Coordinates
Tape 4: Vin Polar Coordinates

MA6-3 Calculus II: Calculus of Several Variables
Part III: Partial Derivatives
with Herbert I. Gross (M.I.T.)
6 B/W videotapes
English
Complete 6 tape set - $600
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: n-Dimensional Vector Spaces
Tape 2: Calculus of Several Variables
Tape 3: Directional Derivatives
Tape 4: The Chain Rule
Tape 5: Integrals Involving Parameters
Tape 6: Exact Differentials

MA6-4 Calculus II: Calculus of Several Variables - Part IV: Matrix Algebra
with Herbert I. Gross (M.I.T.)
5 B/W videotapes
English
Complete 5 tape set - $500
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Linearity Revisited
Tape 2: The "Game" of Matrices
Tape 3: Inverting a Matrix
Tape 4: Inverting More General Systems of Equations
Tape 5: Maxima and Minima in Several Variables

MA6-5 Calculus II: Calculus of Several Variables
Part V: Multiple Integration
with Herbert I. Gross (M.I.T.)
5 B/W videotapes
English
Complete 5 tape set - $500
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Double Multiple Sums
Tape 2: The Fundamental Theorem
Tape 3: Multiple Integration and the Jacobian
Tape 4: Introduction to Line Integrals
Tape 5: Green's Theorem

Calculus III is the last session of the Calculus Series MA5 and MA6. This final part of the course covers complex variables, differential equations, and linear algebra.
The complete course includes: 20 black & white videotapes.

Please Note: For an accompanying Textbook please go to www.Amazon.com and search for George Brinton Thomas. You will find a selection of helpful books.
Part I - Complex Variables
Part II - Differential Equations
Part III - Linear Algebra

Please see the following for individual videotape titles.

MA7-1 Calculus III: Calculus of Complex Variables, Differential Equations, and Linear Algebra
Part I: Complex Variables
with Herbert I. Gross (M.I.T.)
5 B/W videotapes
English
Complete 5 tape set - $500
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: The Complex Numbers
Tape 2: Functions of a Complex Variable
Tape 3: Conformal Mappings
Tape 4: Sequences and Series
Tape 5: Integrating Complex Functions

MA7-2 Calculus III: Calculus of Complex Variables, Differential Equations, and Linear Algebra
Part II: Differential Equations
with Herbert I. Gross (M.I.T.)
7 B/W videotapes
English
Complete 7 tape set - $700
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: The Concept of a General Solution
Tape 2: Linear Differential Equations
Tape 3: Solving the Linear Equations L(y)=0; Constant Coefficients
Tape 4: Undetermined Coefficients
Tape 5: Variations of Parameters
Tape 6: Power Series Solutions
Tape 7: Laplace Transforms

MA7-3 Calculus III: Calculus of Complex Variables, Differential Equations, and Linear Algebra
Part III: Linear Algebra
with Herbert I. Gross (M.I.T.)
8 B/W videotapes
English
Complete 8 tape set - $800
Individual tapes $110.00
Also available on DVDs, call for pricing

Tape 1: Vector Spaces
Tape 2: Spanning Vectors
Tape 3: Constructing Bases
Tape 4: Linear Transformations
Tape 5: Determinants
Tape 6: Eigenvectors
Tape 7: Dot Products
Tape 8: Orthogonal Functions