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h ,0 %Text: Calculus, by Finney and Thomas, AddisonWesley, 1990, Chapters 1115.
1. Vectors and analytic geometry in space. The dot and cross product. Lines, planes and central quadrics. Cylindtrical and spherical coordinates.
2. Vectors valued functions and motion in space. Derivatives and integrals. Projectile motion. Arclength. The unit tangent, the unit normal, and the curvature.
3. Double and triple integrals, change of order of integration, and calculation. Moments and centers of mass. Triple integrals in cylindrical and spherical coordinates.
4. Vector fields. Various kinds of line integrals. Flux integrals. Green's theorem. Surface integrals. Stokes's Theorem and the Divergence Theorem.
There were also fourteen Mathematica demonstrations and eleven Mathematica assignments.
11. Vectors and, ,Analytic Geometry, ,in Space
11.1 Vectors in the Plane 691
11.2 Cartesian(Rectangular) Coordinates
and Vectors in Space 700
11.3 Dot Products 710,
11.4 Cross Products 718 4f(1,2) classes
11.5 Lines and Planes in Space 24
11.6 Surfaces in Space 731
11.7 Cylindrical and Spherical Coordinates 741
For Your Review 746
Practice Exercises 747
12. VectorValued Functions
12.1 VectorValued Functions and Space Curves 751
12.2 Modeling Projectile Motion 762
5f(1,2) classes
12.3 Arc Length and the Unit Tangent Vector T 771
12.4 Curvature 776
For Your Review 795
Practice Exercises 795
Test 1 one class
2.2 Modeling Projectile Motion
13. Partial Derivatives
13.1 Functions of Several Independent Variables 799
13.2 Limits and Continuity 808 3 classes
13.3 Partial Derivatives 814
13.4 Differentiability, Linearization 823
13.5 The Chain Rule 833
13.6 Directional Derivatives, Gradient Vectors, and
Tangent Planes 841
13.7 Maxima, Minima, and Saddle Points 853 6 classes
13.8 Lagrange Multipliers 864
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Practice Exercises 873
14. Multiple Integrals
14.1 Double Integrals 877
14.2 Areas, Moments, and Centers of Mass 887 5 classes
14.3 Double Integrals in Polar Form 893 Test 2
14.4 Triple Integrals in Rectangular Coordinates 899 1 class
14.5 Masses and Moments in Three Dimensions 906
14.6 Triple Integrals in Cylindrical and Spherical
Coordinates 910 3 classes
14.7 Substitutions in Multiple Integrals 919
For Your Review 927
Practice Exercises 927
15. Integration in Vector Fields
15.1 Line Integrals 931
15.2
5 classesVector Fields, Work, Circulation, and Flux 937 Test 3
15.3 Path Independence, Potential Functions, 1 class
and Conservative Fields 946
15.4 Green's Theorem in the Plane 954
15.5 Surface Area and Surface Integrals 965
15.6 Parametrized Surfaces 975
15.7 Stokes's Theorem 983
15.8 The Divergenc Theorem 993
For Your Review 1001
Practice Exercises 1001
7 classes
Divergence
111: Principles of Calculus
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'`'`'` '`h'`h'`hE is a terminal calculus course designed for students who need a basic understanding of the principles of the calculus. Course material includes basic properties of functions, followed by the differentiation and integration of funtions. Some manipulative skills will be required, but this course is not intended to prepare the student for more advanced work in calculus.
3 credits: 2 lecturs and 2 recitation sections per week.
Textbook: Calculus and Its Applications, Sixth Edition
Goldstein, Lay and Schneider
Sample Syllabus:
Sections 0.1 0.6
Sections 1.1 1.8
Sections 2.1 2.3 & 2.7
Sections 3.1 & 3.2
Sections 4.1 4.5
Sections 5.2 & 5.3
Sections 6.1 6.3
Rationale: If Notre Dame is to have a mathematics requirement for everyone and if it intends to admit a certain number of very weak students, there is a need for a course which takes these students and tries to accomplish two aims. The first is that they should see something of the beauty and power of mathematics in everyday use, and secondly they should be encouraged to develop their skills at an appropriate rate. The proposed course does this by requiring four hours a week with the instructor from these students, and by utilizing examples whose nonmathematical principles are easy to understand. The extra hour per week will enable the instructor to cover a standard one semester calculus curriculum.
This class will be listed in DART as for "First Year of Students Only" and the Department intends to teach but one section with limited enrollment.
0 FUNCTIONS, 3
0.1 Functions and Their Graphs, 3
0.2 Some Important Functions, 22
0.3 The Algebra of Functions, 31
0.4 Zeros of FunctionsThe Quadratic Formula and Factoring, 37
0.5 Exponents and Power Functions, 46
0.6 Functions and Graphs in Applications, 55
1 THE D!AEbBbpEQqr58;Bw&'(),./014<?@a67:<> !3!4!Z!\!]!"""#6#7#n###$&$'$d$%W%s%%%%%%%%&&6&7&8&9&:&C&K&L&M&N
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1.1 The Slope of a Straight Line, 72
1.2 The Slope of a Curve at a Point, 84
1.3 The Derivative, 92
1.4 Limits and the Derivative, 103
1.5 Differentiability and Continuity, 114
1.6 Some Rules for Differentiation, 121
1.7 More About Derivatives, 128
1.8 The Derivative as a Rate of Change, 134
2 APPLICATIONS OF THE DERIVATIVE, 157
2.1 Describing Graphs of Functions, 158
2.2 The first and Second Derivative Rules, 173
2.3 Curve Sketching (Introduction), 189
2.4 Curve Sketching (Conclusion), 199
2.5 Optimization Problems, 207
2.6 Further Optimization Problems, 218
2.7 Applications of Calculus to Business and Economics, 230
3 TECHNIQUES OF DIFFERENTIATION, 249
3.1 The Product and Quotient Rules, 249
3.2 The Chain Rule and the General Power Rule, 261
3.3 Implicit Differentiation and Related Rates, 268
4 THE EXPONENTIAL AND NATURAL LOGARITHM FUNCTIONS, 287
4.1 Exponential Functions, 288
4.2 The Exponential Function ex , 292
4.3 Differentiation of Exponential Functions, 299
4.4 The Natural Logarithm Function, 305
4.5 The Derivative of ln x , 311
4.6 Properties of the Natural Logarithm Function, 316
5 APPLICATIONS OF THE EXPONENTIAL AND NATURAL
LOGARITHM FUNCTIONS, 325
5.1 Exponential Growth and Decay, 326
5.2 Compound Interest, 340
5.3 Applications of the Natural Logarithm Function to Economics, 347
5.4 Further Exponential Models, 355
6 THE DEFINITE INTEGRAL, 373
6.1 Antidifferentiation, 374
6.2 Areas and Riemann Sums, 386
6.3 Definite Integrals and the Fundamental Theorem, 398
6.4 Areas in the xyPlane, 413
6.5 Applications of the Definite Integral, 424
functionslectures
and calculation. Moments and centers of mass. Triple integrals in cylindrical and spherical coordinates.
4. Vector fields. Various kinds of line integrals. Flux integrals. Green's theorem. Surface integrals. Stokes's Theorem and the Divergence Theorem.
There were also fourteen Mathematica demonstrations and eleven Mathematica assignments.
11. Vectors and, ,Analytic Geometry, ,in Space
11.1 Vectors in the Plane 691
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