Geology 351- Geomathematics (419 Brooks Hall)
Tom Wilson, rm 231 Brooks Hall - Office hours: 11:15 to 12:15 TTH

3 credit hours – spring 2017

Course Background

Mathematical concepts and applications reviewed in this course cover the gamut of math skills from algebra through basic integral calculus. An important component of the course will be the training you receive in the use of basic scientific spreadsheet/calculation and plotting software (EXCEL). We will spend several hours in the computer lab learning to use these software packages to solve basic problems from the field of geology. This experience alone should be of help to you on homework assignments in your other geology classes (hydrogeology, geophysics, paleontology ...). Download course Syllabus

Prerequisites - 

Geology 351 is offered only to geology majors as an alternative to Math 156 and does not fulfil an elective requirement for the minor. Geol 351 builds on your prior experience with algebra, trigonometry and calculus.  Geology 351, for the most part, employs math skills you already have and introduces new concepts that will be helpful in future geology classes, as well as calculus or other math classes.

Geology 351 provides a review of math basics and use of spreadsheets to develop problem solving, data manipulation, and plotting skills useful in other upper division geology classes. Geol 351 provides several examples of math applications in geology.

The course provides a review of mathematical methods in geology with an emphasis on geologic examples. You will find that Waltham’s text Mathematics: A simple tool for geologists will serve as a useful present and future reference text. Problems taken from Waltham will give you the opportunity to refine and sharpen your mathematical and EXCEL skills.

Be prepared to discuss and work through problems together, but  clearly outline and explain your individual work and approach. This ensures you will be successful on exams.

Stay up-to-date! Check the academic calendar at & final exam schedule


Office Hours: Generally available for questions following the Tuesday and Thursday classes from 11:15 to noon. Check with  via email to arrange alternative meeting times.

  It is essential that you attend class and keep current with reading in the text.

  All assignments, laboratory exercises, etc. are due at the start of class.

  Late Homework Policy: There is a 10% deduction for homework not handed in when due. An additional 10% will be deducted for each additional day late thereafter. Homework assignments will not be accepted once that assignment has been returned and discussed. I usually have homework back the following class period. This rule will be strictly enforced unless you provide an official university excuse. If you miss class, you can complete inclass worksheets and receive up to 50% credit if completed and submitted the following class period.

   The midterm Exam counts 20% and final in-class activities also count 20%. While the final requires skills developed over the semester, the main focus final activities will be on materials covered in the last half of the semester.

 For daily lecture content see table with links below

Visit Tom's GeoMath channel, your Mathbff and Kahn Academy
Having trouble solving that equation - visit WolframAlpha

general content Reading/Problems Assignment
1. (Jan 10th)  First Day Activities:  Some problems concerning sea level rise, water use, and shrinking ice caps that illustrate contemporary quantitative applications in geology. See In-class problem set related to intro materials (Chapters 1 & 2). Order now! For more about the text and author visit Waltham's page.
Order your book ASAP! Begin looking through chapters 1 and 2 of Waltham and the in-class problems
Sea Level variations in the Grand Isle area and Excel basics: Video 12 and 3.

2. (Jan 12) Introduction I: Elementary mathematical relationships in geology. Group Problems;
Units conversion examples and answer key ( click here )

Chapters 1 and 2 of Waltham (pages 1-38). Video discussiond of subscripts 1, exponential notation 2, and linear relationships 3.

3. (Jan17) Introduction II: Expressing relationships between geological variables.  Today's group problems2 for review.
Chapters 1 and 2 of Waltham (pages 1-38). For a reminder on the assumptions made in these simple equations see youtube video.

4. (Jan 19) Math Relationships continued. Have a look at basics.xls (for a quick tour of the basics.xlsx file, see this video) and additional problems for group discussion today. Another in-class problem.

5. (Jan 24)  Using Excel to solve problems 2.11 and 2.12: slides and Computer Lab 1:
  Problem Presentation Format & related concepts associated with the North Sea problem. For a more detailed view of the North Sea data analysis see videos part 1 and part 2.
Discussion of Archie's law part 1 and 2. The physical relationship of F to porosity.Video discussion of why F decreases as the porosity increases.

Chapter 2 problems 2.11 and 2.12
Excel analysis of north sea data from Video related to part iii) in the computer lab:  calculating the intercept.  
6.(Jan 26) Today's discussion reviews mathematical models covered to date, introduces the Fourier series and introduces problem 2.13. See Computer Lab 2 (will be handed out in class) which will cover use of Excel to solve problem 2.13 and general radioactivity decay problems. See Step2.xls and have some fun with Fourier Series. Today's in-class activity.
Chapter 2 problem 2.13; add 2.15 to the homework assignment. YouTube video review of the in-class activity.

Video discussing logrithmic transformations of exponential functions: Parts 1 and 2. This youtube video guides you through the in-class activity.

7. (Jan 31)Discussion of radioactive decay problem 2.13 continued with general discussion slides; Some in-class problems associated with exponential functions.Video overview of exponential decay and growth problems discussed in class.
8. (Feb 2) For the day: Review exponential decay and growth relationships, their solution, intercept determination, organization of presentation and basic equation manipulation.This Excel file provides several worksheets that illustrate the population problem and series approximation of the base e (see Ln_Expansion.xlsx). An in-class problem related to isostatic equation manipulation;  and consider problems 3.10 and 3.11 for group discussion next time. Visit this useful site for units conversion.
Read Chapter 3: look over problems 3.10 & 3.11.

Video presents some background on the development of Stoke's law. 
9. (Feb 7) Isostacy:  The basics of equation manipulation illustrated using problems in isostacy. Try this in-class problem. Look over this additional problem take-home isostacy problem concerning isostatic adjustments during long term erosion. We will discuss in class next time and turn in. Questions about problems 3.10 and 3.11 worksheet handed out last time?  Due at end of class today.
Continue your reading Chapters 3 & 4
practice equation manipulation skills by trying to derive all isostacy relationships given in today's handout.
10. (Feb 9) More on Isostacy, then Computer Lab: Roots of quadratics and operator preference issues (for reference only); see also Quad.xls. We'll spend most of our time on Stokes Law and the settling velocity problem. Turn in problems 2.13 and 2.15. Turn in book problems 3.10 & 3.11. Readings: Chapters 3 and 4

11. (Feb14) Slides for the day. Final questions on the settling velocity problems? Introduction to evaluating which mathematical model provides a good representation of your data with computer lab. See fitting lab guide
  • Settling velocity Excel problems due  Tuesday 23rd.
  • Problems 4.7 and 4.10 due March 1st
  • Fitting lab due March 3rd.
Getting close to midterm  Test coming up ... start preparing

Start reading chapter 8
12. (Feb16) Midterm grades and general reminders. We'll go over the fitting lab activities in detail.  The practice mid-term exam will also be distributed.  The settling velocity lab is due today. Please hand in before leaving.
You should be able to make a lot of progress on this today
13. (Feb21) Pre test review (slides):  Practice Exam Questions 
Pre-midterm review ...
14. Mid Term Exam  (February: Thursday 23rd, rm 325 Brooks Hall) Mid Term Exam held in rm 325

15. (Feb 28) Post-test discussion. Final questions and review of fitting lab activities.  Get started reading Chapter 8
16. (Mar 2) Slides for the day. Complete the fitting computer labHand problems 4.7 and 4.10 before leaving. Hand in fitting lab activities along with problems 4.7 and 4.10
Spring Break (Mar4  through 12)

Introduction to Differential and Integral Calculus
17. (Mar 14)Some initial thoughts on derivatives. Have a look at these problems for discussion and consider the slopes of common functions.  Start working through these example derivative problems.
Continue reading Chapter 8.
18. (Mar 16) Derivatives continued - Lecture Overheads (continued):  Visualize your formula at WolframAlpha & also see See Excel examples in limits.xls. Finish in-classbasic differentiation problems and basic differentiation rules. Some self-assessment questions
Finish reading of Chapter 8
19. (Mar 21) Lecture Overheads:  Discuss derivatives of exponential and logrithmic functions.  Self review derivatives worksheet  (this is not  a homework assignment, but does provide opportunities for additional practice).   Problems 8.13 and 8.14 from the text . Self assessment 2 to be worked in class.
Chapter 8: look over problem 8.8, page 148 and problems 8.13 and 8.14. Bring questions to class next time.
20. (Mar. 23) Slides for today.  See Excel examples in limits.xls. Introduction to Excel Derivatives Lab. Computer problems 8.13 and 8.14 with  a reference sheet to help you with the Excel setup. We'll get started on these today Questions about  the self review problems (handed out last class).Text problems 8.13 and 8.14 are due next Tuesday.
21. (March 28th) Some lecture slides. Self review continued.  Discussion of problems 8.16 to 8.18. Some additional material on maxima and minima. Another solver problem: locate the angle that minimizes work expended during faulting. Need some extra practice with derivatives? The trendline. For some additional practice with derivatives, try these problems. Derivatives in reverse. Look over today's handouts - group exercises 1 and 2 - for next time.    Turn in 8.13 and 8.14
Begin reading Chapter 9: Integral calculus.
22. (March 30th) General slides.  Introductory discussions of integral calculus (the antiderivative or derivative in reverse).  Derivatives in reverse - group exercises 1 and 2 Turn in Excel problems 8.13 and 8.14
       Continue reading Chapter 9
23.  (April 4) Work through all those antiderivatives (indefinite integrals and read through Chapter 9. Refresh basic integration rules/skills. Get ready for Chapter 9.
24. (April 6) Introduction to Integral Calculus:   Definite and indefinite integrals. Calculating lithostatic and hydrostatic pressure at depth. Some simple calculations using Waltham's integ.xls file. Introduce an integration problem related to fault propagation folding. Will spend time in class in groups but not due till next time.  In class integral assessment problems - hand in before leaving.

25. (April 11) More practice with integration  - Return and discuss assessment questions. Questions concerning lithostatic/hydrostatic pressure computations and the fault area/shortening problems.   Bar sand volume problem Question 9.7 to be handed out.  Some additional  integration problems will be handed out for practice.  We'll work in groups if time permits.  Start looking over Problems 9.9 and 9.10. Get started on computer problem 9.7
26. (April 13) Integral Calculus (continued):  Return to the group integration problems from  last time and discuss.  Questions on the fold shortening problem.  Questions about the volume of Mount Fuji problem as discussed in the text?  In-class effort to set up Excel version of problem 9.7 handed out last time.   General discussion with in-class discussion of setup for Excel version of problem 9.7.
27. (April 18) Slides for the day: General discussion of integration problems. In-class integration problem. Continue work on Excel problem 9.7. Integration of discontinuous functions. Brief introduction and discussion of problems 9.9 and 9.10. If time permits, we'll go over some additional problems on heat flow and consider some self assessment problems  Look over problems 9.9 and 9.10 for next time.  Questions on 9.7?
 Grade summary. Begin Exam review. Look over materials covered in Chapters 8 and 9. Start getting questions together for next week's review sessions. 
28. (April 20) Slides for the day.  Questions on problems 9.9 and 9.10. We also look at a final review problem and some in-class problems. If time permits we'll look at the spreading ridge mass problem. Next week's in-class problems will the review problem format and also that of an initial in-class/take-home activity that will be handed out today and will be due next Tuesday. We will get started on this one today.Hand in problem 9.7. Hand out take-home final activity 1. Due next Tuesday.

Final in-class group activities

29. (April 25): Take-home/in-class activities begin today Some general slides for reference  
Turn in Excel problem 9.7. Also turn in problems 9.9 and 9.10. In-class/take-home problems sets 1& 2
30. (April 27): Brief slides for the day. Turn in volcano volume and slope analysis at beginning of class. Final in-class/take-home activity. Reference slides and review from last week may be of interest. Turn in Tuesday's problem. Hand out in-class/take-home problem 3
Exam schedule  - 5-7pm, Thursday, May 4th    final exam schedule

                                                 Additional Applications/Topics of interest  
lecture notes Integral Solutions Some additional perspectives on problem solving with integrals

Gravity problem - Possible in-class take home problem (non calc).
1. Trigonometry - Introduction: lecture slides - problem assignment Questions about 9.9 and 9.10 Read Chapter 5
2. The 3 point problem, vector concepts and manipulation: Lecture slides; In-class problems (2). Excel File illustrating vector computations  
3. Trig review with in class problems; questions about the homework in Chapter 5.  
                                                              Statistics Read Chapter 7
4. Lecture Overheads: Intro to Statistics with in class computer exercise  
5. Lecture Overheads: Working with probability tables and accompanying EXCEL Exercise  
6. Lecture Overheads: Review - Probabilities, statistical error and significant differences  
7. Computer Lab: Using the t-test to evaluate significant differences Chapter 7: Problem 7.13, Read Ch. 8
                                 Pump tests, flood recurrence & landscape evolution  
8. Working pump test data in Excel. Estimating maximum sustained yield from pump test data. Discussion and Handout:  
9. Etimating flood recurrence intervals  
10. Landscape Evolution  

 11. Spectral analysis presentation 1 and Step.xls. Spectral analysis presentation 2 and  Wrap up chapter 9 discussions  
Comments on in-class/takehome stats exercise & final problem set  

Some Web Resources

Need an Algebra Review? Practical Algebra Lessons
Lithosphere loading: Airy and Pratt. Isostatic Compensation. - Example problems
Compaction Porosity/Depth Relationships and Sediment Compaction -
  A problem to think about.
Decompaction Backstripping -
  Problem set
Gutenberg-Richter relation frequency/magnitude
fractal interrelationships Fractals:
fitting data to a straight line Linear Regression