Sharon K. Robbert, Professor of Mathematics

 

Christianity and Mathematics Devotionals connected to mathematical content  Single-variable Calculus | Multivariable Calculus | Discrete Structures  Linear Algebra | Differential Equations | Statistics Multivariable Calculus   Devotional Title Course Topic Scripture References Our Common Parameter:  Christ Parametric Equations Gal 3:26--28 Approximations and Intentions Planar Approximation to Surfaces I Corin. 13:12 Stratification in Christ's kingdom? Level Sets Colossians 3:10--11, Romans 12: 6--8 Where Are You Headed? Vector Function Derivatives Prov. 22:1-8 Building on the Past Dot Product & Polar Coordinates Acts 17:16-24 Portrait of God Consistent extentions of 1-variable content Deut. 6:1-9 The Span of God's Love Plane Equations Eph. 3:14-21 Following Directions Partial Derivatives Joshua 24:14ff No Inconsistencies allowed! Local Linearity, theory of the derivative Romans 2:17-29 The Israelite Matrix Matrix arithmetic Numbers 2 Successive Generations Higher-order derivatives Exodus 20:4-6, Gen 22:15-18 Be Extreme for Christ Extrema of functions in R3 Rev. 3:14-22 One Body, Many Gifts Multivariable chain rule Eph. 4:1-13 Constrained Optimization on Easter Constrained Optimization Matt 27:50-54, 28:1-7 Explaining Predictions Limit of sums definition of the double integral Luke 24:13-32 Measurements Iterated Multiple Integrals measure volume 2 Chron 4:1-5 Living Sacrifices through Transformation Change of variable and Jacobian Romans 12:1-2 True Reflections of God Area magnification factor Exodus 33:12-23, 34:29-35 Our Common Parameter: Christ Gal 3:26--28 Christ is our common parameter. back to top Approximations and Intentions I Corin. 13:12 Sometimes, analysis of a given relationship in multivariable settings is complex--too complex to be worth the effort of exact calculation. Instead, it is sufficient to use an approximation for the relationship that matches some but not all of the essential characteristics of the original relationship. This is modeled below by the planar approximation for the lumpy surface. To calculate values of the lumpy surface, we instead find a simple function (here a plane) that in a small window around the point the values will agree within some tolerance for error. A Planar Approximation to a Lumpy Surface This idea is somewhat like the relationship between the original beauty of God's creation and the world we see today. We are unable to see clearly the goodness--we see only in a "mirror dimly"  the approximation to the perfect creation intended by God. This gives us hope for what the new creation will be like when Christ returns again in glory! back to top Stratification in Christ's kingdom? Colossians 3:10--11, Romans 12: 6--8 In the three-dimensional images you see above, the location of the hills and valleys are easy to see. Not quite as easy to see in the diagram are the saddle points that lay diagonally between two valleys and two hills. To better understand the characteristics of a function, students use level sets, a collection of two-dimensional graphs which gives detail about slices of the function using regularly spaced heights. At left is a portion of the level sets for the lumpy surface above. The hills and the valleys in the level set plot are at the centers of the concentric "circles" while saddle points occur at the intersection of the boundary lines. This idea of grouping the function input values by output values is a little like the stratification we see daily in human culture. There are those who are perceived to be at the highest level (e.g., Michael Jordan, Queen Elizabeth II) and those who we see at the bottom of the deepest valleys (e.g., death-row inmates, Al Qaeda terrorists). However, we learn in Colossians 3:10--11 that in Christ there is no such ranking. "Here there is no Greek or Jew, ." and all Christians must "put on the new self, which is being renewed in knowledge in the image of its Creator." However, Christians are not clones of each other. Each is given a different configuration of spiritual gifts. In this type of stratification, we rejoice in the distinctive service we can provide for God's kingdom. back to top Where Are You Headed? Prov. 22:1-8 Acceleration/velocity for paths of life back to top Building on the Past Acts 17:16-24 Paul connects "unknown god" to Jehovah.  Building on existing ideas to understand something new. back to top   Portrait of God Deut. 6:1-9 One true God.  His character is consistent even through He is too complex for us to understand.  Not the God described by Muslims or mystics--deviate character. back to top The Span of God's Love Eph. 3:14-21 Span of God's love (plane is the span of two vectors) back to top Following Directions Joshua 24:14ff Follow directions that God set (partial derivatives) back to top   No Inconsistencies Allowed! Romans 2:17-29 Must be continuous Christians--no inconsistencies back to top The Israelite Matrix Numbers 2 the "matrix" of Israelites during the Exodus. back to top Successive Generations Exodus 20:4-6, Gen 22:15-18 successive generations--higher-order derivatives back to top Be Extreme for Christ Rev. 3:14-22 Jesus knows what we perceive as strengths; not hot nor cold so rejected. back to top One Body, Many Gifts Eph. 4:1-13 Distribution/dissection of spiritual gifts strengthens the whole church (the chain rule) back to top Constrained Optimization on Easter Matt 27:50-54, 28:1-7 The Easter story (Death = min -> Life =max) Our constraint curve was away from the maximum, Christ moves it to the perfect place! back to top Explaining Predictions Luke 24:13-32 Jesus appearance on the road to Emmaus to explain OT predictions to disciples--limit of sums definition of the double integral back to top Measurements 2 Chron 4:1-5 Measurements back to top Living Sacrifices through Transformation Romans 12:1-2 Be transformed, living sacrifices back to top True Reflections of God Exodus 33:12-23, 34:29-35 Moses radiant face, transformed to reflect God. back to top Project Overview Devotionals connected to mathematical content  Single-variable Calculus | Multivariable Calculus | Discrete Structures  Linear Algebra | Differential Equations | Statistics back to top  skr--Spring 2003	Robbert Profile Math Triathlon Christianity & Mathematics Vita
Mathematics | Sharon Robbert | Triathlon | Christianity & Mathematics | Vita