Lectures for Advanced Calculus One, MATH 4530

Here are the lectures for Advanced Calculus One or MATH 4530. We will use my notes for this class which will be published next year in book form. The notes cover both MATH 453/653 and MATH 454/654 so you can see what the next class will cover if you want to look ahead. BasicAnalysisOne-08142019.pdf

Here is our syllabus. syllabusm453653-S2019.pdf

Here are sample exams.

First Sample Exam 1 exam1-fall16-A.pdf
First Sample Exam 1 Solutions exam1-fall16-Awsolns.pdf
Second Sample Exam 1 exam1-fall16-B.pdf
Third Sample Exam 1 exam1-fall16-C.pdf

First Sample Exam 2 exam2-fall16-sampleA.pdf
First Sample Exam 2 Solutions exam2-fall16-sampleA-soln.pdf
Second Sample Exam 2 exam2-fall16-sampleB.pdf
Third Sample Exam 2 exam2-fall16-sampleC.pdf

First Sample Exam 3 exam3-fall17-sampleA.pdf
Second Sample Exam 3 exam3-fall17-sampleB.pdf
Third Sample Exam 3 exam3-fall17-sampleC.pdf

First Sample Final Exam final-fall16-sampleA.pdf
Second Sample Final Exam final-fall16-sampleB.pdf

Here are the projects

Project One: presentation style ProjectOne.pdf
Project One: handout style ProjectOne-handouts.pdf
Project One MatLab Code Plottingh.m
Project Two: presentation style ProjectTwo.pdf
Project Two: handout style ProjectTwo-handouts.pdf
Project Two MatLab Code LOneEnergy.m
Project Two MatLab Code Sample Data FittingData.txt

Here are matlab files we use.

DrawGrid.m DrawGrid.m
DrawMesh.m DrawMesh.m
DrawTraces.m DrawTraces.m
DrawBase.m DrawBase.m
DrawColumn.m DrawColumn.m
DrawPatch.m DrawPatch.m
DrawSimpleSurface.m DrawSimpleSurface.m
DrawTangentLines.m DrawTangentLines.m
DrawTangentPlanePackage.m DrawTangentPlanePackage.m

Here are the presentations in pdf form. You can save them on your local drive or view them in your browser.

L1: Mathematical Induction I L1-MathInduction.pdf
L2: Mathematical Induction II L2-POMIAgain.pdf
L3: Non POMI Proofs and Triangle Inequalities L3-NonPOMIProofs.pdf
Errors for Lecture 3 in Text errorlog3
L4: Upper and Lower Bounds L4-Bounds.pdf
Errors for Lecture 4 in Text errorlog4
L5: Sup and Inf Results and Sequences L5-SupsInfsSequences.pdf
L6: Convergence of Sequences L6-SeqConvergence.pdf
Errors for Lecture 6 in Text errorlog6
L7: Algebra of Limits and Bounded Sequences L7-LimitTheorems.pdf
L8: The Bolzano Weierstrass Theorem for Sequences and Infinite Bounded Sets L8-BolzanoWeierstrass.pdf
L9: The Bolzano Weierstrass Theorem for Sets and Set Ides L9-BZForSets.pdf
Errors for Lecture 9 in Text errorlog9
L10: Compactness L10-Compactness.pdf
L11: The Limit Inferior and Limit Superior of a Sequence L11-LiminfLimsupSeq.pdf
L12: More Sets and Topological Compactness L12-TopologicalCompactness.pdf
L13: More Topological Compactness and Limit Inferior and Limit Superior of functions L13-MoreTopCompact.pdf
L14: More Limit Inferior and Superior of Functions and Limits of Functions L14-MoreLimInfLimSup.pdf
L15: Dirichlet's Function, Lack of Continuity Example using limit inferior and limit superior, the definition and right and left limits. L15-DirichletFuncLimitsCont.pdf
L16: More continuity sample problems and the algebra of limits and algebra of continuity theorems L16-MoreLimitMoreContExamples.pdf
L17: Consequences of Continuity L17-ConsequencesOfContinuity.pdf
L18: Lower SemiContinuity and Convexity L18-LowerSemicontinuityConvex.pdf
L19: More Convexity and Subgradients L19-ConvexityAndSubgradients.pdf
L20: Our first taste of derivatives L20-Derivatives.pdf
L21: More on Derivatives L21-MoreDerivatives.pdf
L22: Even More on Derivatives: the Product and Quotient Rule L22-EvenMoreDerivatives.pdf
L23: Function Composition and the Chain Rule L23-ChainRule.pdf
L24: Sin and All That L24-SinAndAllThat.pdf
L25: Rolle's Theorem, the Mean Value Theorem and Function Approximation L25-RollwithMVT.pdf
L26: Function Approximation and Higher Order Taylor Polynomials L26-FuncApproxs.pdf
L27: the Number e L27-TheNumbere.pdf
L28: The Exponential Function and Taylor's Series L28-ExponentialTS.pdf
L29: More On Exponential Functions, Inverse Functions and Derivative Consequences L29-InverseFuncsLogs.pdf
L30: More Inverse Functions and Logarithms and L'Hopital's Rules L30-LHopitalsRule.pdf
L31: The First and Second Derivative Test L31-FDTandSDT.pdf
L32: Limits and Continuity for functions of 2 and 3 variables L32-LimitsinRN.pdf
L33: Surfaces, Tangent Planes and Partial Derivatives L33-SurfacesAndPartials.pdf
L34: Derivatives in 2D and 3D and the Chain Rule L34-RNDerivatives.pdf
L35: Tangent Plane Error and the Hessian L35-TPandError.pdf
L36: Conditions of Partial Derivatives to Imply Differentiable L36-DiffResults.pdf
L37: Constrained Optimization: Lagrange Multipliers and Optimal Values L37-ConstrainedOpt.pdf
L38: Extremal Theory for Functions to Two Variables One L38-TwoVariableExtremaI.pdf
L39: Extremal Theory and Signed Definite Matrices L39-PositiveDefiniteIdeas.pdf
L40: Exponential Matrix Solutions to Systems of ODEs L40-LinearSystemODE.pdf

Here are the presentations in a form better for printing. There are two presentation pages per printed page so the number of pages you need to print is a lot less.

L1: Mathematical Induction I L1-MathInduction-handouts.pdf
L2: Mathematical Induction II L2-POMIAgain-handouts.pdf
L3: Non POMI Proofs and Triangle Inequaliies L3-NonPOMIProofs-handouts.pdf
L4: Upper and Lower Bounds L4-Bounds-handouts.pdf
L5: Sup and Inf Results and Sequences L5-SupsInfsSequences-handouts.pdf
L6: Convergence of Sequences L6-SeqConvergence-handouts.pdf
L7: Algebra of Limits and Bounded Sequences L7-LimitTheorems-handouts.pdf
L8: The Bolzano Weierstrass Theorem for Sequences and Infinite Bounded Sets L8-BolzanoWeierstrass-handouts.pdf
L9: The Bolzano Weierstrass Theorem for Sets and Set Ideas L9-BZForSets-handouts.pdf
L10: Compactness L10-Compactness-handouts.pdf
L11: The Limit Inferior and Limit Superior of a Sequence L11-LiminfLimsupSeq-handouts.pdf
L12: More Sets and Topological Compactness L12-TopologicalCompactness-handouts.pdf
L13: More Topological Compactness and Limit Inferior and Limit Superior of functions L13-MoreTopCompact-handouts.pdf
L14: More Limit Inferior and Superior of Functions and Limits of Functions L14-MoreLimInfLimSup-handouts.pdf
L15: Dirichlet's Function, Lack of Continuity Example using limit inferior and limit superior, the definition and right and left limits. L15-DirichletFuncLimitsCont-handouts.pdf
L16: More continuity sample problems and the algebra of limits and algebra of continuity theorems L16-MoreLimitMoreContExamples-handouts.pdf
L17: Consequences of Continuity L17-ConsequencesOfContinuity-handouts.pdf
L18: Lower SemiContinuity and Convexity L18-LowerSemicontinuityConvex-handouts.pdf
L19: More Convexity and Subgradients L19-ConvexityAndSubgradients-handouts.pdf
L20: Our first taste of derivatives L20-Derivatives-handouts.pdf
L21: More on Derivatives L21-MoreDerivatives-handouts.pdf
L22: Even More on Derivatives: the Product and Quotient Rule L22-EvenMoreDerivatives-handouts.pdf
L23: Function Composition and the Chain Rule L23-ChainRule-handouts.pdf
L24: Sin and All That L24-SinAndAllThat-handouts-handouts.pdf
L25: Rolle's Theorem, the Mean Value Theorem and Function Approximation L25-RollwithMVT-handouts.pdf
L26: Function Approximation and Higher Order Taylor Polynomials L26-FuncApproxs-handouts.pdf
L27: the Number e L27-TheNumbere-handouts.pdf
L28: the Exponential Function L28-ExponentialTS-handouts.pdf
L29: More On Exponential Functions, Inverse Functions and Derivative Consequences L29-InverseFuncsLogs-handouts.pdf
L30: More Inverse Functions and Logarithms and L'Hopital's Rules L30-LHopitalsRule-handouts.pdf
L31: The First and Second Derivative Test L31-FDTandSDT-handouts.pdf
L32: Limits and Continuity for functions of 2 and 3 variables L32-LimitsinRN-handouts.pdf
L33: Surfaces, Tangent Planes and Partial Derivatives L33-SurfacesAndPartials-handouts.pdf
L34: Derivatives in 2D and 3D and the Chain Rule L34-RNDerivatives-handouts.pdf
L35: Tangent Plane Error and the Hessian L35-TPandError-handouts.pdf
L36: Conditions of Partial Derivatives to Imply Differentiable L36-DiffResults-handouts.pdf
L37: Constrained Optimization: Lagrange Multipliers and Optimal Values L37-ConstrainedOpt-handouts.pdf
L38: Extremal Theory for Functions to Two Variables One L38-TwoVariableExtremaI-handouts.pdf
L39: Extremal Theory and Signed Definite Matrices L39-PositiveDefiniteIdeas-handouts.pdf
L40: Exponential Matrix Solutions to Systems of ODEs L40-LinearSystemODE-handouts.pdf

Author: Dr. Peterson, Mathematical Sciences, Clemson University
Last Updated: August 22, 2017
petersj@clemson.edu